I don't know if you've ever been to Asia, but I get the impression that the difficultly there is that vegetarianism isn't as common as it is in North America or Europe and people aren't as familiar with it. ??? I've only been to Japan and I found it difficult because fish and to a lesser extent other meats are often found in dishes where it's not readily apparent, for example as broth. Friends have given me the impression that China is a hard place to be vegetarian, but who knows.
That said, my dad's wife grew up in Laos, which is of course closer to the parts of Asia you're interested in, and she never has problems making me vegan things. Granted, they got married after I left for college, so she doesn't make me food all the time.
I have done an abroad volunteering program where the volunteers were almost all english, american, european or canadian, and they were used to seeing a lot of vegetarians, so it was no problem. I'm sure that once you look closer at different programs you can ask them about eating vegan whereever you'll be staying. Unless of course you're meant to be feeding yourself.