Do you have any specific tips for photography in the mountains?

Yes. Don't carry too much kit. Usually in extreme environments you are limited by both weight and time. Ideally have a single versatile set up. Make sure you preserve battery life. Never switch a camera on when the battery is cold, warm the battery first. Avoid post processing and review on the camera which drains battery life, and carry spares.

Try and have some foreground in your landscapes. I remember sharing photos after a successful climb of Chulu Far East and when I showed a mountain scene to one of my climbing colleagues he said "I stepped over that plate of bright red Chillis to take that view". Now it may be you prefer it without the Chillis, and it wasn't the best photo in the world, but I would recommend at least considering what you can get in the foreground before you take your photo.

In bright environments, such as snow, use a polarising filter if you can and either shoot exposure bracketed or slightly underexposed to preserve any contrast better. I find some versions of post processing software are better at "brightening" photos than "darkening" photos.

Don't be surgically attached to your tripod, often you will be shooting at high shutter speed in bright light and a steady hand capturing a fleeting moment may be more important than a rock steady platform.