IMO, it's definitely smart to leave it in place. After all, it's not like we get a lot of rain, even in the winter!

The mulch will allow the rain to soak into the soil more evenly and slowly, help prevent erosion and add decomposed organic matter to the soil.

Speaking of mulches, this post reminds me how irritated I often get with gravel mulches. My dislikes: it doesn't improve the soil at all; if you want to plant in it, it's heavy to rake away to make a bed or a planting hole; and my biggest complaint is that it eventually becomes pushed into and embedded into the top soil layer. So if you want a nice soil planting surface without gravel, one's forced to take a screen and sift all of the gravel out of the soil. (in fact, I was doing this yesterday for a bit. A big pain in the a#$...) Well, I guess you all know how I feel about gravel mulch now :)

On the other hand, I can't talk favorably enough about organic mulches (as long as you know they require a bit more extra nitrogen fertilizer to compensate for their decomposition needs...)

Good points:
Helps prevent roots from freezing by insulating. For most deciduous trees that is not a problem. For evergreens that survive freezing not a problem because their canopy protects their roots down below. For trees that are not cold hardy, die back and can grow out again from rootstock I'd say a thick layer of organic mulch (wood chips) is indispensable.

As was said, organic mulch breaks down adding a slow release fertilizer effect to the tree. But this process is slowed down in the winter.

Bad points:
We get 3" of rain on average in the Dec-Jan period. A layer thicker than 4" can block water from absorbing onto the ground immediately below. I don't really consider this a problem.

If you are using frost cloth part of the trick is to let the ground heat up in the daytime. It may be best to pull the mulch back from the dark ground in winter and let this solar process happen. [can inspect underling drip irrigators too as spring approaches] But a decomposing mulch pile generates some heat that would help in the evenings under a frost cloth, so. . . .

Pulling mulch away prevents rodents overwintering in it next to the tree. I have not had a problem with this but it is common problem in other states.

For the most part, I'd leave it in place. keeps the ground from getting to cold and maintains soil moisture.

My only caution on leaving the mulch in place is that it's a breeding ground for grasshoppers and ticks, maybe others but those are my personal experience. I've let the debris from the Lady Banks and thevetia's collect under the hedge-rows thinking the mulch was good for the plants. Unfortunately, I'm now dealing with a tick problem on my dogs.

I've known for a while the 'hoppers are probably coming from there but I've created a barrier around the raised beds to keep them from hopping in. The dogs have been bringing in ticks for about 8 weeks now. The recent temp drop should kill them for the season but we're planning to rake out all that litter (mulch) before spring. Just sayin'...........

Thanks for the input everybody -- I've always left it in place, but began to second-guess myself after reading and hearing that mulch "should" be removed before the onset of winter.

I'm wondering if that advice applies to cooler climates.

PS - Agree about the gravel "mulch" - never understood how a layer of hot pebbles baking in the desert sun could be considered mulch. Why not pour concrete and call it "maintenance free mulch"!