I'm not a contractor but I would have my doubts. Call the inspector and don't allow work to start.
If your foundation isn't right to start with you're in for a lot of headaches!

Here is a link that might be useful: Concrete

Cold weather concrete pouring requires several precautions, none of which your contractor appears to have done. Normally this would be a clear violation of the contract but I suspect it doesn't contain a concrete specification if you let the contractor write it.

In the circumstances you describe it is doubtful that the concrete was able to hydrate enough to be structurally sound.

I don't know the structural requirement of this concrete but if it is supporting a building I would require the contractor to cover the concrete and heat it for a week in the hope that the error could be corrected.

Your local building inspector should be concerned about this unless he is a pal of the contractor.

Relying on a contractor or building inspector for construction quality control is not wise IMHO but you have a lot of company in that regard.

Thanks folks, that helps. I have checked the reference as well as other sources and you are right on.

I checked weather records and it has been 80 hours since the pour and the temperature has been in the 20s (some periods in the teens) all that time, except possibly for 3-6 hours, but never got past 32-33.

Is it certain that this concrete will fail? Is it still possible that it will have enough strength for its intended use (one-story kitchen space). How can I tell/prove that the concrete is failing or if it does not have enough strength? Is there a test or instrument or something?

My friend has sent email to contractor to advise him of situation, at least to get it on the record.

If we called county inspector, can he/she even tell something is wrong by looking at it?

The most reliable way to determine the strength of the concrete is to cut a sample cylinder and test it to failure in a lab. Less reliable non-destructive methods are ultrasonic pulse velocity and rebound hammer. These tests are performed by an engineer from a company that does quality control testing. The tests are more reliable after 28 days.

If an anti freeze additive was in the mix, it should be no problem. Ask your contractor if it was in the mix, I dont know why any outfit would not include it this time of year in freezing areas.

The use of so-called "anti-freeze" accelerating admixtures that reduce the setting time, increase the rate of early-age strength development, and increase the heat of hydration are no excuse for not protecting the concrete from extreme cold weather.

If enough calcium chloride was used to save the work it might also cause excessive drying shrinkage and corrosion of reinforcement.