Great Wall safety on cold icy days

Is it possible to go to the top of the Great Wall during cold winter days or is it dangerous and not allowed?

Yes it is possible to visit the wall on cold, icy snowy days.

Won't be much fun though

Our adult children are only able to visit us during winter break. I Guess it will be more of a bucket list item being checked off.  We will go this weekend then again first week of January.