Any of several mp3 players will do. The ever popular iPod Touch for example. I'm not a fan of Apple's iTunes software but their players do have nice screens for viewing videos and photographs (and plenty of internal memory for those video clips).
The altitude won't be an issue but the extreme cold will be. Low temperatures play havoc on the battery life of electronic devices. (That goes for his camera, phone, etc., too.) And obviously delicate electronic devices don't respond well to being slammed around.
So if the mp3 player will be in the backpack, buy or improvise a hard case. The screen will always be a weak point, no matter how rugged the rest of the device is. Simply wrapping the mp3 player in a sock might not provide sufficient protection.
If he'll be away from civilization (i.e. recharging opportunities) for just a few days, he can also consider keeping the mp3 player close to his body. As an added benefit, his body heat will prolong the battery life. If he'll be away for a week or more, the backpack it is. And in that case also add a solar charger to the budget.
Solar charger come in various models. There's everything from fancy small ones like this http://www.solartechnology.co.uk/freeloader-solar-chargers.htm for $80, to DIY jobs like this: http://yosemiteoutside.com/m/Blogs/02EA4A6B-8893-4F3E-87A8-C1E4B24C3AAB.html
I'm sure you'll get more good suggestions here, but for further input try posting this question in the Consumer Electronics section.
---
BB, iPod Touch models use flash memory instead of hard drives, so no worries.
http://en.wikipedia.org/wiki/IPod_Touch#Specifications
---
InTheShadows, the iPod Touch also has a lithium battery :-)