When the Zamboni passes over the ice, it scrapes off a small layer and then lays down some new water to freeze and smooth out.  They dump all that scraped ice (snow) snow out the back of the arena.  If you are cool about it, and go inside to ask the rink manager, they will usually let you shovel a bunch of it into the back of a pick up truck.  Sometimes, they will even dump it in the back of your truck for you.
Just make sure you ask, because if you just start shoveling, they can get a little ticked.
And Conner is just joking about bleeding, spitting and puking on the ice...he is too small to play hockey.