Two reasons I can think of. One, the alsohol makes you go so deeply unconscious that you lie in the same position all night and are stiff as a result, or two, your hollow legs are going rusty.
Could be gout - that is often brought on by alcohol (especially red wine, port etc) althoughI believe it is more likely to afflict the big toe first in that case.
Perhapes its related to what you do whilst you are drinking - standing at bars for long periods, excessive disco dancing, crawling home on all fours ;-) Seriously, worry pains in my left arm turned out to caused by me 'playing' my electric guitar - something I only venture to do whilst drunk.