you can cut grass any time the weather is mild and dry - I often pop out and do it in that window that usually occurs around early January. If you're not using a hover mower, it can cause mud smearing, and that might look messy. Hard to say if there's lasting damage, depends whether you've got sunken, compacted areas from the workmen, and of course, we can't see it...

I agree with bamboo that you can cut grass when the weather is mild and dry. I always cut it when there's a spell of weather like that right through the winter. I have been lucky enough to have had plenty of chances lately, and hope to have more to come (fingers crossed), and my grass has been fine! ?

You'll probably find the grass goes a bit brown where the footprints were but it will recover. Grass doesn't grow when the temp is below 45 degreed F and there's not a lot you can do about that! If you do get conditions when you can cut it use a longer cut than you do in summer as the grass grows more slowly in cold weather and cutting too short would weaken it if it couldn't grow back. Think more about the grass being healthy than what it looks like for now. Pity you didn't add your county to your profile as conditions vary a lot from north to south.

It really depends what kind of "damage" you are talking about. A picture or 2 would be helpful. We are in late November, the garden needs to rest, it's all going to sleep.