What are some ways to make a mountain climb interesting?

I want to make my party climb a massive mountain (think like K2 massive) for the next part of my campaign and I'm looking for some ways to make the actual journey more interesting. The party is fairly high level (level 11 to be exact) so things need to be very difficult. They don't have any spellcasters (only a paladin) so they don't have any game-breaking magic readily available but they do have a Fairy which has a constant flying speed for something extra to consider.

I plan on potentially throwing a few Adult White Dragons at them and maybe a short dungeon in there for some substance but I kinda wanna get some more interesting ideas than just constantly doing increasingly difficult skill challenges. Anyone got any ideas for me to steal?