It is really not an issue. You can run portable furnaces in the house if there is a particular concern. If the house is all closed up, it usually will stay pretty warm inside although you could be in Maine or Alaska.

The only issue with the cold is pouring the foundation. People tend to work outside slowly in the cold but there is nothing you can do about that.

Agree with David Cary. The only time there might be major concerns would be when pouring cement (if no additives for cold pour were in the mix), drywall mudding/finishing in very cold environment(yours is complete I believe) and after water service to house has been established (late in the building process).

Most likely your new home will not have it's heating system operational until near the completion of the entire house. I don't forsee any problems other than possible personal discomfort of subcontractors working in a cold house which could always be taken care of by portable heaters.

Typically the general contractor won't be asking the utility provider(s) to hook up their meters until they are almost complete with the home... maybe a couple of weeks prior to certificate of occupancy.

Where I am (British Columbia, interior) it's pretty much SOP to use construction heaters - gas, or temp electric, once they start to insulate if it's cold, I guess to dry everything - then through the drywalling and mudding process.

You should check what's standard in your area - if contractor seems on the ball, he/she may be right, but you're correct, it's probably getting close to being needed.

Like I said, temp heating is easy to organise. If you go for propane or diesel, make sure there's adequate ventilation.

If there is no water yet, no.

It would have to stay below freezing for several hours (or leaving the windows open) for the pipes to get cold enough to freeze.