Assuming you are shooting digitally, a polarizer should be all the filter you really need. This can reduce contrast in the scene my making the sky darker, depending on the angle of the sun. It will also reduce glare from the snow.

You may also consider a solid ND filter if you wish to do long exposures. You can do this to include climbers are night as they trace paths through the mountain with their lanterns or head-lamps. Since you get a clear view of the sky at altitude, you may also do star-trials.

Facing mountainous terrain, there is little use for a graduated ND filter since the transition on the filter is unlikely to match anything natural in the scenery. Instead, you can probably experiment with exposure fusion.

If you are shooting film, then you can add a Skylight or UV filter to reduce the blue tint caused by high-altitude UV rays. Digital sensors no not have the UV problem and compensate for tint via white-balance which you can get manually to get perfect results.