Thanks for the tips about the cold weather package. This caused me to look it up and it appears that for 2011 models if it has the heated seats and steering wheel then it has the cold weather package which means it also has the battery warmer. I agree, this seems essential.
I would be storing it in a heated garage at night, so that does help.
As jlv says, I should be able to recharge fully in 4 hours given my relatively short commute. So it's possible that most or all of my weekend driving could be covered by Friday's 8-hour charge at work.
The point about my personal tolerance for risk is quite pertinent. At a low enough price, the risk is worth it for almost anyone, but it's a different price for each of us. I need to figure that out for myself. One useful metric is total cost per mile assuming worst case I won't be able to resell it after 7 years.
I'm realizing insurance is a useful factor in removing some of the financial risk. If the car gets totaled, it's likely insurance will partially make up the difference. I'm trying to determine just how much that would be. The worst case financial scenario is likely if the battery fails rapidly and spectacularly, or a component fails that requires specialized electrical skills and parts to fix.
But in my situation it's unlikely the battery would deteriorate rapidly enough to prevent my 14-mile daily round trip. Say after 7 more years it dropped to a 15-mile range, it would still work for my purposes, but resale probably wouldn't be possible. I'm hoping I can sell it after 7 years for ~$1,000 but with the way they depreciate who knows, it might be $100.
My crazy idea depends on the car needing little to no maintenance for the rest of its useful lifetime, and due to the electric motor the Leaf is about as close as I could hope to get to achieving that.
Another thought is that perhaps Nissan will eventually start selling and supporting electric cars in Alaska due to pressure from Tesla (there are ~15-20 Teslas here), and I'll be able to get the battery replaced locally at some point if needed. The future is all electric, it's just a matter of when. Of course if anyone is going to be laggards, it's going to be Alaska.
Thanks everyone for your helpful observations and input. I need to mull it over a bit more and compare total costs to a hybrid alternative, but right now I think there's a pretty good chance I'll take the risk.