Does a person "refresh" the dirtholes and make look like fresh digging for coyotes or leave them as is?

I would freshen the lure, but as far as freshening up the dirt you can do either. Making it look like fresh digging will give good eye appeal though, just don’t spend too much time at the set. Use a stick or piece of brush to scuff the dirt up like a coyote was digging and leave. The more time you spend the more scent you leave.
Or you can just leave them be. Neither way is wrong and I’ve caught coyotes with both

Leave as is. They already know they are there. Check from a distance. New, light snow over sets creates interest.

I like if there is snow on the way and I know it.
I will spray antifreeze the pattern and the hole.
That really makes them stand out in a field of white
Just what works for me

I agree with what Hern said. I think a light snow gives canines more confidence to check out the set.