I live in WI and would rather have saved the $$$ and got the front wheel drive, but all that is available up here is AWD. My experience has been that AWD or 4 WD for that matter does not matter as much as the tires on the vehicle. I had a Lexus GX470 that was AWD and I could lock the differential to make it true 4 WD. It originally had Bridgestone Dueller tires on it, and no matter what, I was slipping, sliding in the winter and hydroplaning in the summer. I took those off in under 20k miles and put on Michelin Cross Terrains and the problems went away. Same thing with my wifes Sienna minivan (which is only FWD).... Came with crappy Good Year tires, and she had no winter traction in light snow, and terrible wet road performance. Switched out the Good Year for Michelin latitude touring (which came on my JX) and the difference was night and day. Her traction in the snow was not far behind my Lexus and wet traction was excellent. So.... IMHO, save your money and go with the FWD.
As a caveat, I don't think that the AWD on the JX is that intelligent, as I still get some tire slip in the front wheels if it's wet out and I floor it.....