Why would you insist on riding with your hands behind your back, or crossed over your chest, or just hanging by your sides when I caution that you need to keep at leat one hand connected to the bike unless your wiping off sweat or getting a drink?
raindrop, I'm not challenging what you said, I'm sincerely requesting more info. I routinely during cool-down, or if there is a quick reprieve between songs, will sit all the way up on the bike (i.e., no hands) and spin, usually with my hands at my side or on my hips. I'm especially inclined to do this after a more intense track, as I find the position allows me to "open up my chest", breathe better and bring my HR down a bit. Is this really a bad thing? (several people in the class tend to do it, and the instructor has never said otherwise). I wouldn't dream of doing this while standing.