Update: my camera is not so crappy, after all
Okay, so I fiddled with the settings a bit. Obviously I need a tutorial on what my camera can and can't do. I'm sure it's capable of more than I think, although it is a bit old by now. I set it to manual, low light, and slowed the exposure way down. I think this shot, while it doesn't show that much snow, is still really beautiful:
But if you want proof of snow, see here: