Avalanche snow isn't a fluid; I'm pretty sure it isn't typically going to get forced down your throat, and definitely not into your lungs.

But if the snow is dense enough, you still will run out of air eventually.

According to this study, most people buried in avalanches do die because they run out of air, but it sounds like it's a lot slower than drowning, so there is a better chance for rescue if people get to you soon enough.