I bought a pda for when I go mountainbike touring. I can use this both for reading and I also use it to store routes on digital maps.
If you need backlighting then a pda probably is the best bet (although of course reading an 'eink' reader with a head torch could be an option).
I'm afraid I don't know what battery life in the cold is like, but spare batteries are reasonably cheap and light. Normal battery life is about 8 hours reading on the lowest backlight setting. Haven't yet had got a solar charger or used it with one.
You probably don't need more than a ziplock plastic bag to keep it in, but you can get ruggedised waterproof casings from 'Otterbox'.