I did the same thing, went over huge mound of snow, but it had a chunk of ice from the other storm. Made a loud noise when it hit the frame but no damage. Just kept on truckin'.

 

You answered your own question... As the other guys said, with less surface area you get more pounds/square inch. Do you want your girlfriend to step on your hand with the heel of her stillettos or her sneakers??

This, of course is an overgeneralization. Would I rather have a 6" wide summer tire or a 8" wide all terrain? The AT obviously, but given the same tire... I'd take the skinnier one.