Part of my yard was dug up for utility work. They filled it in and put sod down. I'm in US Midwest and winter is upon us. The low temperatures have just recently begun dipping below freezing, highs are still above though. Should I water the new sod? If so how much water and for how long?
Timing's important, it's not clear how long ago the sod was put down, but as your weather is now turning wintry, it would not be a great idea to water it. In any case, if the landscaping company actually did water it for two weeks after laying, if that was, say, only a month ago, then hopefully it shouldn't be a problem. If they laid it a longer time ago, then it may have gone short of water, but its really a bit late to worry about it now, if your temperatures have already started dropping below freezing. If it looks like its suffering from lack of water, and you get a reliably milder period of 3 or 4 days, then it's probably worth watering during that gap in the weather, but otherwise, its wait and see what it looks like in spring.
UPDATE You've said the sod was put down the day you asked the question, which means they'll be back to water it on a regular basis for the next two weeks. If your weather is or becomes very cold day and night (below freezing) in that time, don't let them keep watering, but as long as that doesn't happen, let them do it. After that, presumably it will be colder, so don't water then other than during milder spells of weather and only if it needs it - it might not.
Have you tried pulling it up by grabbing the grass to test if it had enough time to put roots into your soil? If it is firmly rooted, you have a good chance that your sod will survive. If you get a day of warmth or rather a few hours where the water won't freeze immediately go ahead and water and water deeply. Try to get at least 2 - 3" deep into the soil wet. That will be the last watering for the winter.
If you are unable to get a shovel into the soil easily you are probably past the window but I'd go ahead and water at least once when it is sunny and above freezing. If you think about it, there are lots of lawns and winters are sporadic and sometimes it warms, rains and waters your lawn anyway. And I've never run into 'rain damage' caused by rain on frozen soils/lawns.
Another thought is what happens when we get snap freezes during the growing season. It isn't the freeze that damages tender plants like those in a vegetable garden, it is how fast the frozen plant cells thaw. When you've had a freeze and you've got frozen cells and then the sun comes up to quickly thaw those cells, that is when you have damage. To reduce damage I go out before the sun comes up and start watering. This helps to slow the thawing and bursting of cells. For your situation, the grass blades that are far more tough than vegetables thaw in the sunshine and when you water there should not be a huge change in temperature that will cause plant cells to burst. If you water when the blades are frozen you are more likely to cause temperature change too quickly and damage some of the still photosynthetic green blades. But that won't kill your grass, it'll just brown it more quickly and cause some stress, that you should try to avoid. Kind of the reverse of watering to slow damage from an unusual freeze during the growth season. But there is a problem with frozen grass most people don't know...
The mistake people make during cold, freezing weather is WALKING ON THE GRASS! Even with hard frosts, walking on frozen crowns (the transition between the blades of grass and their roots) will break and kill the grass. You'll see footprints in the spring. So stay off the sod and forget about fertilizer until spring.