I see. So its partly anatomical. So theoretically, some breeds would survive the winter, assuming they instinctively took to burrowing.
Except I dont know what the actual biological processes are for wild rabbits that hibernate. I dont actually know that any pet breed would have them 'built in'.
And the population issue, as you mention. I would think they wouldnt be very successful mating, since they look so different than wild ones, but sometimes I guess some rabbits find odd things attractive. Plus, I dont actually know how successfully different breeds can mix.
So the fur and breeding issues become apparent. I am still curious if pet breeds can in fact hibernate; if is some biological, internal requirements, or simply instinct behavior.
Now I am thinking of Bunny Island in Japan, and wondering what their story is, how did they adapt. I dont imagine it has much winter, so it doesn't really address hibernation I guess.http://www.odditycentral.com/pics/okunoshima-island-japans-rabbit-paradise.html
It clearly showcases the overbreeding you mentioned. I've heard the rabbits are very gregarious.https://www.youtube.com/watch?v=2ixspJ-SnMk