So, here's the scoop. After I found this question, I was actually really curious if it would work, so I went and tried it out. The Snow Golems deal little to no damage to the Ender Dragon. So I guess it could be possible, BUT the Snow Golems attack ANY hostile mob, so even while you want the to try to kill the Ender Dragon, they will attack the Endermen as well. So it might be possible, but it would take a very long time for it to actually happen. Another downside is that whenever the Ender Dragon sweeps in, the Snow Golems are pushed out of the way, so most of the time they fall off, or are killed, and never get a chance to land a shot on the Ender Dragon.