One of the keys to avoid having the snow slow you down is to run faster.
You can also get down real low and position your face so that it is near the snow. As you exhale, slight amounts of snow will melt, lessening the total snow depth. In that manner, you can also dramatically advance how fast you can go per a given amount of effort. I think I read that in a dream somewhere, so that's how you know it's very good information you can use.
There is a Buddhist saying, "Wisdom can be found by feeling the breath through your toes." If you could find that wisdom, you wouldn't have to get down real low.
Around here the sub-morons have a saying, too: "When the rattlesnake is about to bite your hand, put the snake in your other hand."
Not recommended with a snow snake, however.