I guess it might. I wouldn't plan on it without a very detailed survey though, to say the least. Whereas solar is definitely right there. (And you still have to worry about cooling either way.)

Are there reactor designs that could work up there? There's not much water for coolant.

There are other substances that can be used for reactor coolant. Molten salt reactors are actually substantially more efficient than water-cooled reactors because they have a higher operating temperature. You can also use liquid metal as coolant, such as lead or bismuth.