Your camera gear should generally be fine in alpine winter conditions. The main issues are usually cold-related battery loss and condensation when moving from freezing outdoors into warm indoor air, not elevation itself.

Helpful precautions:

• Put the camera/lenses in a sealed zip-top bag before bringing them indoors. This helps moisture condense on the bag instead of on the camera or lens.
• Let the gear warm up gradually to room temperature before taking it out of the bag; this can take an hour or two.
• Carry one or two spare batteries in a warm inside pocket. Cold reduces lithium battery performance, but warmed batteries often recover enough for more shooting.
• If practical, keeping the camera under your coat can help preserve battery life, but be careful if you’re sweating or moving between temperature layers, since moisture can become a problem.

In short: cold weather itself is usually manageable, but control condensation and keep batteries warm.