I used to play with a towel looped through my front belt all the time. Surprisingly, it doesn't get in the way of your swing. A Golf Digest editorial I once read said that you'd never see a professional doing this. My response to this was, "Yeah, but professionals use a towel many, many times throughout a round. It just so happens they have a caddy to manage the towel for them.
Having a towel on you is helpful so many times for wiping your hands, your club, and your ball on the green. My irons were always in great shape because I gave them a quick wipe after every shot.
Just watch: the next thread will be one on pace of play in which people are complaining that the guy in front of them kept going over to his cart to use the towel hanging from it. 🙂