I ride with headphones blasting...when I'm on my trainer staring at a wall all winter.
Personally I prefer hearing all the sounds of my bike and my breathing when I'm out on the road. Plus it's nice being able to hear cars coming up behind me so I can pull further into the shoulder as a courtesy.
I always ride with a helmet when I'm training, but I think I'm going to start taking it off on climbs cause I just get too damned hot. I was thinking of clipping it under my seat in these situations, any suggestions? I definitely want to bring my helmet with me for the descent at the very least.