Is it possible to change your facial features in game?

No. So choose wisely.

Damn. Now I'm stuck with some bearded chump.

There is one thing you must absolutely learn about this game. You must know if you are dissastified with your character early on. If you are, delete him ASAP so you don't get really dissapointed for having a high level character you hate, and have to spend more time levelling a new character.

If you are unhappy, change it now before it gets really bad.

Also note that some races change the eye color around as you select that race during character creation. My dwarf went from green to blue to brown, just at random when I kept selecting the race.

I restarted my troll like 6 times trying to get a skin color that wasn't blue or purple. I thought I had grey, but settled on a green (which was still blue under a lot of lights).

It's true WoW is lacking in that department. And with warcrafts' manga-fantasy style if you choose a beard and big nose it looks twice as blocky in-game so watch it, lol. Some games (especially MMO's) now allow you to change physical appearance for a small fee/task/quest etc. Devs are finally catching on that there is a reason for 'chronic-rerolling'.

I wanted to point out a really bizarre experience with facial features in an entirely different game. I played Silent Storm, a tactical turn based WW2 game, and it had a really awesome face generator. The bizarre thing was that you would almost never zoom in that far to see that you gave your guy a French royalty shaped nose or high cheekbones. It was like they were seeing if anyone noticed. This should be one of the first things that an RPG should pay attention to - especially one with a lot of investment in individual characters. And this is not to mention heights and weights. Items make you look pretty distinctive though, eventually.

As is, my lead character, a Troll, looks kinda like Weird Al Yankovik, even with a big green mohawk and tusks lol. When I noticed that around level 15 I wasn't overjoyed haha.