I played 36 at Saucon Valley Old and Weyhill back in 02 in the middle of July, walking, and wearing pants as i was told I had to. We started early, but it was well over 90 (with very high humidity) for most of the day. My two friends and I counted that we each drank 18 bottles of water or gatorade, and one of them still felt sick and had to lie down after we finished. Luckily the club's pool is about 20 yards from the 18th green at the Old course, as we were in it 90 seconds after putting out.
The no shorts rule is pointless, the only thing that can happen is someone is stupid, doesn't drink enough water, and passes out on the course. Forget tradition, its just common sense.