This is a perfect example of where tankless units fail miserably; that water is expected to heat the water quickly as the GPM constitutes that motion and if the water is considerably colder, that temperature swing is dramatic which equates to less of a desired temperature than the unit is set to.

Same applies to your tank water heater. ANY water heater, whether 30/50/80, it doesn't matter; there is a 12 gallon rule. Meaning, the capacity of your tank will always have 12 gallons less water that is "ready to use" than the capacity itself.

Why? Because it takes 12 gallons of cold water entering the tank to move the ready to use hot out of the tank before temperature fluctuations occur. There's absolutely no way to pull full capacity out of ANY tank made for this reason that it takes incoming cold to get the hot to come out.

Now, in winter time where cold climate weather is common, this affects ground temperature. In Ohio the ground hovers around 60 degrees in summer. In Arizona in the highest heat of the year their ground temperature is considerably warmer. In Indiana right now with the outside temperature of 10 degrees, this drops the ground temperature to around low 40's.

This prolongs the heating cycles of your water heater to satisfy the temperature settings dictated by the thermostat. If the water is colder, the cycles are longer. This is the time of year where water heaters go kaputz because if they are on the fringe so to speak with corrosion and rusting with thin spots in the tank, this time of year will cause them to leak/fail.

I can't advise the idea of turning up the thermostat because licensed plumbers (in my area) are not allowed to turn the thermostat above 120 degrees. No exceptions. You take the risk of scalding/skin burns when you take it above 120 considerably.

If you are using the tank with the chance that the heater is operating in the midst of a cycle, this could be the reason why. Instead of 40 minutes to create a tank of ready to use hot water.....the lowered incoming cold water temperature is now forcing that same heater to heat water for 55 minutes to satisfy the temp settings.

Based on the description of the problem, it could be that the bottom element is not heating. If that is the case, the element itself is probably the culprit. It is entirely possible that the onset of the colder weather and the simultaneous failure of an element are just coincidences. With perhaps 50 million or more water heaters in this Country, any combination of events involving the heater is statistically possible.

It could certainly be the incoming cold water temperature (although from my perspective, here in Wisconsin, your "20's" sound like a walk in the park LOL). But I think it's also important to know, how old is your tank? Age could be a factor. And, the tanks sold today are so much better insulated than those from even just a few years ago. But your problem could also be sediment build-up. From the Bradford White website: "As water heaters age, they tend to accumulate sediment and lime deposits. If the heaters are not cleaned periodically, the sediment may rise to a level that will act as a barrier between the burner and the water, making it harder to heat. An article published in a national ASPE plumbing journal states: for every half inch of sediment on the bottom of a gas fired water heater, it requires 70% more fuel to heat the water.

I've linked below to a thread in which I asked how to clean sediment from my hot water heater.

Here is a link that might be useful: Forum Thread on How to Clean Sediment from Tank

I would get a jacket for the heater or a new water heater. I am hardly ever installing water heaters anymore, Tankless water heaters are becoming the standard around here. I only am familiar with the rinnia. I put one in my unheated garage and it gets alot colder than 20 here. I bought a cheap white cabinet at home depot and insulated the inside with 2" foam board and then mounted rinnia 2532 commercial unit inside. A glass of water will freaze sitting next to the cabinet. For the first time my wife and I can both take showers and run the dishwasher at the same time. And i have it set at 130.
About a block away and about 3 years ago i installed a 2520 rinnia on the outside of my nieghbors house. They have never had a problem and have all the hot water they want.
I am a tue believer in Rinnia.

Just some follow-up notes:

1. The water heater in question is 10 years old.
2. It is a natural gas water heater.
3. It has an additional insulation jacket I installed years ago.
4. I've routinely flushed the water heater (averaging about every other year) and did so sometime in the last year (note that I'm one of the contributors in the above mentioned link on how to flush a hot water heater).

As a side question on flushing the water heater, when ever I do so, I get out these semi-opaque bluish gel-like pebbles (1/8" to 1/4" diameter). What exactly is that? (Note that we live in an area with VERY HARD water.)

peteyboy, I'm in Texas, two counties in from the central coast area. We don't typically have temps into the 20°Fs or lower, but 30°Fs do sometimes occur for several days, like during the arctic blast earlier this month. I'm on a private well. The well & pump are at the front corner of my property. The tank is in my detached garage, wayyyyy around the other side of the property. Anyway, during said arctic blast and several days after, initial incoming water was approx 40°F. After running a while to purge the LONG supply line from pump to tank, then tank to house, with fresh flow, it'd creep up to ~50°F. My electric tankless had no trouble outputting 115°F, 130°F, or even 140°F at a reasonable flow-rate. For 130°F, it'd typically run at 70% of full output, so there was still sufficient reserve capacity for higher output temps or higher flow rates.

Tankless units are expensive compared to tank
Electric tankless are expensive to wire and operate.
The good ones (Rinnai) are expensive units because of their quality.

All tankless units are very expensive to repair when the down the road issues arise. I won't buy the nonsense that they are expensive as tank heaters. At the most, $80 swing either for electric or gas.

Finding someone with trained hands in your area to work/maintain tankless repairs are hard to find. Otherwise you are subjected to days, not hours without hot water and you are also depending on items shipped to you if you are capable of diagnosis, repair of your unit.

The MAJORITY of homeowners have tank heaters, that's a fact. Salesmanship of trying to get the homeowners to spend thousands instead of 100's when the heater goes kaputz is putting personal finance in priority to customer's needs.

Meaning that if you do not disclose the periodic maintenance of a tankless (deliming/descaling to heat exchanger to prevent efficiency loss) as required by most mfg warranties to stay intact, you are misleading the flock.

The end user of such product needs to be fully aware of all parameters involving these units and understand that no one is coming over with a thermocouple or set of Robertshaw thermostats to fix their unit. It's more and more expensive.

So if you have such tastes for steak when everyone is eating hamburger, expect the obvious. If money isn't a problem and got tons to spend, tankless is for you.

There's a reason why homeowners never maintain their water heater and never think about it until the hot water quits coming out. They also go down the laundry list of plumbers trying to get the best price of how much to spend, usually under a grand. The majority DO care about quality, but cost is usually the driving force of MOST matters concerning heaters.

That's why they price 4 different heaters from 4 different mfgs with the best deal.

Jump on the tankless bandwagon and now you've isolated yourself from others that get their hot water back in hours, not days. Hopefully you of those that have tankless have in-area support when it breaks down.

In my region they don't exist, the rep is usually out west or they swing it to a plumbing company as an authorized rep to keep replacing parts till it works.

With ground water temperatures lower, it will take longer for your water heater to recover during cold weather.

That being said, even though you've been regularly flushing your tank, with very hard water, and after ten years, you probably have a big chunk of solidified sediment at the bottom of your tank. No amount of flushing will remove this, and it makes the efficiency and recovery rate of your water heater go way down.

Even though your tank isn't leaking, it may be time to replace the water heater. You may also want to move up to a slightly larger tank. Most households with kids now go with a minimum 50 gallon tank.