Just thought I'd shed some light into why people are being stingy over the snow lords. I was playing my Taxibot today when the shout went out that one had spawned in Four Seasons. I ran over there, died, but got ressurected in time to help take him down. I got the experience, I got the snowballs, and I got the present...but I got no badge. I sent a petition inquiriing why, and I was informed that because neither I nor my team did the most damage I didn't qualify for the badge.
So, unlike other Monsters, you actually have to be part of the team that does the most damage to get the badge. If, for example, you are on a team of 8 level 12's and some level 50 comes along and out ranks you on the damage? That hero is going to get the badge and your team isn't.
I know for a fact Babbage doesn't work this way, because I took part in a mass assault on him that involved about 30 heroes and we ALL got the badge.