I learned to deal with it climbing towers. If vertigo starts to set in, you stare at the rusty bolts and try to figure out if you could loosen them with a wrench, or if you'd need an impact tool. Literally, stare at something right near your face... count the carpenter ants or try to teach them sign language... anything that you can concentrate on. When the feeling subsides, slowly move on, thinking only about what you're up there to do, and nothing else. Don't watch the clouds (they move) or look at the ground (thing you're climbing is moving, your brain thinks the ground is, and panics a little) and keep doing that for awhile. Even if you're terrified of heights, if you stay focused on the task at hand, your brain will adjust and teach itself to ignore the height.
Oddly enough, the height doesn't bother me much in a tree. It still does on the roof of a tall building if I get near the edge, and it still bothers me quite a bit on a tower. I have to use the same trick, again, if I haven't been up on those things in awhile. For some odd reason, trees feel safe to me and knowing that the climb line really will hold me is enough that I just ignore the height. I still avoid looking down or at the clouds if I'm nervous (like spurring up a leaning stem, where I feel like I might spin and take a beating on the bark). It's natural to be nervous... helps keep you from thinking you're Tarzan and doing something stupid.