I usually use a <a href="http://www.brasslite.com/">Brasslite</a> alcohol stove. At trail camp last summer, though, I used a butane/propane canister stove (was cooking for a largish group) so I can't speak to that environment specifically. I'm sure I had my alcohol stove there, too, but I don't recall if I used it there; plus, it was probably warmer. I do recall using it in the Cottonwood Lakes area (~11,000 el) on the same trip, and it dipped slightly below freezing there.
Anyway, I have used that stove frequently at 9,000-10,000' altitude and in pretty cold temps (e.g., on PCT at Memorial Day when streams had a layer of ice in the AM).
The issue is whether the fuel will vaporize. Alcohol vaporizes easily, which is why simple soda-can stoves work without pumps, etc. The alcohol also ignites readily so most self-priming alcohol stoves shouldn't have trouble at reasonable altitudes and temperatures.
But I'm not a stove scientist.
Maybe you could fire off an email to <a href="mailto:aaron@brasslite.com">Aaron Rosenbloom</a> at Brasslite and ask him. He'd know for sure and is pretty good about responding to emails.