Birds are particularly sensitive to temperature/sun/drafts/humidity changes. I don't think birds should be taken camping. Actually, I'd be leery about taking any animal camping if you are going off hiking and leaving the animal unattended in a campsite. There are some weird people out there- is it really fair to leave an animal vulnerable to unknown strangers passing by?
So then if not a dog, and not leaving it unguarded in a tent, what animal could you actually take hiking up a mountain with you...bumping around in your pocket or backpack for hours?

I sympathize with your yearning for a pet, but taking pets tent camping is perhaps not safe or fair to them. We should consider the quality of life we can offer to the animal as well as our own needs.
I'd suggest getting the kind of pet that doesn't mind being left alone for a week or two (maybe leave a soft radio on for a warm blooded pet). I used to get a lot of fun and satisfaction from various small creatures as pets- mice, turtles, hamsters, snakes, rabbits, tarantulas (don't laugh, they are fascinating!), fish, finches, crayfish, toads, praying mantids, etc etc.
Even a Venus flytrap plant can be an interesting kind of 'pet'. All these creatures will 'interact' with you, maybe not always on an emotional level.