At the risk of beating a dead horse, allow me to opine based on extensive snow/ice riding experience here and elsewhere in the N.E.
In fresh untracked snow, pretty much any width tire (to Utah’s point) is going to be effective at biting down and achieving decent traction, with width being of increased importance as the trail starts to climb (though all tires will have their limits (fatties included) eventually in this situation, typically at 6” or thereafter).
Similarly, when the trail is FIRMLY packed down EVENLY all around (heavy foot, snowshoe, XC ski, tires, etc), to the point where it is simply a channel in the snow, tires of pretty much any width will suffice.
Where the fattie tires excel is when the snow is unevenly packed/lumpy, and fluffy stuff is interspersed with boot/hoof/showshoe traffic. Each print represents a harder (packed) spot on the trail, with fluffy loose snow around each. When a skinnier tires goes from fluff to these packed spots, the front wheel deflects, causing the rider to have to saw at the bars, which in turn can cause the bike to go off track and/or slide out. A fattie tire is much less likely to deflect and essentially “bridges” the bike’s front end from boot print to boot print, kinda like a steamroller, requiring far less effort from the rider and enabling him/her to stay upright and keep pedaling.
This was the situation this past weekend on many trails, including the one I rode. I was able to ride for 4 hours on 98% of the terrain. If I had ridden a regular MTB, I could have covered about 40%. Despite the few times we get this sort of snow in NJ, this for me was the difference between riding and either staying home or paying $80+ to go boarding. And we all know riding wins
Put another way for those that don’t snow-ride: Think about taking bike with CX tires through a rock garden vs using a bike with regular MTB tires. The former has a higher likelihood of getting thrown off track. The latter would surely be a better experience with a higher degree of success.
