You don't "need" to take any filters. You also don't say what you interested in taking photos of. If I was lucky enough to be doing this trek, I'd take a UV filter for sure (to prevent blue snow colour cast), a circular polarising filter, and if taking sunsets/sunrises, I'd take graduated ND filters of different strengths. I'd also take a tripod for my landscape photos. If I could only take one of those things, I'd take a tripod. Shoot in raw and you can edit as much as you like to mimic the effects of the filters. Good luck with your photos and have a great time!