Well, I didn't wrestle in H.S. but my older brother did and I know that they were indeed done nude.
I did a quick search and it seems that the skin check and weigh-in (which are typically done at the same time) is done differently depending on where you are and what type of event.
I found a few like these that do talk about nude or undergarment weigh-ins:
This one is "underwear or an athletic supporter":
This one is a little different -- it says:
"All contestants, including heavyweights, shall weigh in
wearing no more than an athletic supporter for males and
pants and bra for females."