From what I've been told, woodstoves are considered the equivalent of a camp fire by many jurisdictions. They are therefore not allowed except where open campfires are allowed. Part of the problem is the low wood supply near and above timberline--the land managers want what wood there is to decay and replenish the very thin soils there rather than to be burned. Some jurisdictions may also ban alcohol stoves in times of high fire danger because they can start a fire if spilled.

There is a lot of info to be found on the PCTA and postholer.com websites--if you haven't been there, you'll find a mine of information!