This is what the movie the matrix was all about, depth. How far down the rabbit hole neo was willing to go in order to see what the real world was like, and this was one of the most popular movies in the world in its time. Another thing to note about depth is just how important it is in daily life. This is probably why depth shows up in dreams as often as it does, especially in the case of the symbols of Deep snow.
If you have a dream about deep snow it means that your sense of wonderment has increased. It might have to do with the season you are experiencing. Perhaps winter is coming and this is why you are dreaming of what you are dreaming of but whatever the case is, you are being self reflective and thinking about what could happen and where you are going in life. This is a good thing for you and it means that you will finally get where you need to go in life. You can rest a little bit easier knowing that your sense of reality has gotten better and that at the same time you are exponentially more appreciative of the world that surrounds you. This is a good thing, you need to be happy about it or how else do you expect to get along?
To dream that you are caught in deep snow may also symbolize the fact that you feel as if you are being held back from something. There is something that has been caught in your way and you just can’t get past it. There is literally not one thing you can do and it isn’t even the fault of anyone else so there is no use in getting mad. The good news is, the blockage will go away on its own soon, but in the meantime try not to blow a gasket.