I've built a tree house, it's going well, but I'm worried that mobs burning at dawn could bring the whole thing down in minutes. Is this possible?
No, it's not.
It would be a pretty stupid feature actually since zombies and skeletons burn upon sunrise. You wouldn't have a single tree on the map after day or two. :-D
I started to build Yggdrasil, the world tree, and invested hundreds and hundreds of wood (and many hours). I also went through and made sure there was no lava within 2 blocks of the wood.
It burned to the ground. It was in a shaft that let sunlight in so I'm wondering if it IS possible for burning mobs to set fire to things... I shall build a trap to test it!
Of course, maybe I just missed some lava. I was pretty thorough, though.
UPDATE: At least, according to this walkthrough, they can: http://pc.mmgn.com/Walkthroughs/Minecraft-FAQ