Virginia Creeper will smother and kill the tree, good plan staying away from that.

Alpina clematis is a good option but you would need to wrap a small amount of wire around the trunk. Nothing serious, it will cling when it finds the wire. If you're interested I have a seedling you can have. It'll bloom next year and probably cover a significant amount of a trunk by the 3rd year. LMK if you want it.

I haven't seen it done but William Baffin and Polstjarnan roses are both supposed to be happy scrambling in a tree. They would need both training and support, tying as they go. They are also both large and prickly.

Honeysuckle vines do need support.

Not sure why you'd want to cover a tree trunk: most tree bark is very ornamental.

Honeysuckle will need something to climb on, as it is a twiner. Will Porcelain vine grow up there?

Rick

Just thought I'd mention Smilax herbacea too. It has nice shaped leaves and is native, but *apparently* it smells like dead rats. I don't have a good sense of smell and I've never noticed it. If you get a female plant it has pretty purple berries. I thought mine was perennial but it turns out it regrows quite vigorously each year from underground racemes. I don't look at it a lot but I think it looks quite nice scrambling in my mountain ash.

A quick and easy climber is wild cucumber vine. You might have to give it something to grab onto in the beginning though. It's not perennial, but self seeds, so it comes up again faithfully. The seedlings are easy to pull out where they're not wanted. I like the frothy looking flowers.
But I made a mistake the time I let it grow up my screen in the sun-room. It looked really cool from inside, but the tendrils are like wire and were very difficult to remove from the screen afterward.

Thanks for the suggestions. I think I will hold off and ponder this a bit more before I make any decision.