I've been troubled by obtaining the snow beast as a 1-player battledome challenge.
From the website, the guide told to refresh at advent calendar.
Other than that, actually you can get him from random refreshes at Terror Mountain as well.
However, It's been the 5th day, I set my browser to auto refresh every 5-10 second non stop. I still haven't get it.
And I suspect I did not even get any random events at all, my neopets was fine, and items did not change at all.
Am i doing it right?