snow is an interesting substance....you have to choose whether you want to float or cut through it to reach the ground for traction.
Obviously snow-cats and snowmobiles try to stay on top, but wheeled vehicles tend to need to get down to something with more to it....thus the advent of the tire chain.
if you have super wide tires, you air down to create a larger contact patch spreading out the weight of the vehicle over a larger area, trying to float.
If you have skinny tires and there is Ice under the snow, you need chains to grip it.
Really deep snow say over 2 feet, you probably want to float on it. shallow less than 2 feet, you might want to cut down through....
The reality of it all is that our vehicles tend to end up somewhere inbetween floating and cutting through which makes snow wheeling so challenging!!
sorry for the confusing commentary....your trip looked really fun!!