Over ear, or On ear? Most over ears have a pretty large headband, and thats not nearly as pliable as a beanie is. On ears usually have a thinner headband, but I still would not consider it for underneath a helmet. I used to love skiing with on or over ears, but they do not mix well with helmets.
you should get a koss ksc 75. its a cheap on ear, with comfortable ear clips instead of a headband, that will easily work underneath a helmet. They arent the most durable things out there, but they have unmatched sound quality under $60, and even compete with more expensive headphones. I have like 5 pairs, just because theyre soo cheap ($20) and the quality is great. I also have a lot of experience with high end headphones like sennheiser, audio technica, v moda, denon, grado, shure, among others. the ksc 75 is cheap and sounds very good, and its open back so you can hear whats going on around you, which is good for skiing.