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:
http://www.aausports.org/sports/wrestling/filaRules.htm
http://www.nsaahome.org/textfile/wrest/assessorprotocol.pdf
http://www.jaguarwrestling.org/Handbook_files/FMHS_Wrestling_Handbook.pdf
This one is "underwear or an athletic supporter":
http://www.iesa.org/administration/handbook/IESA-ByLaws-Activity.pdf
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."
http://www.wvssac.org/new_site/wvssac_website/html/Interscholastic/November%202006%20Webpage.pdf