They may very well till it in but they're wasting fuel at any price. The "grabbing N" part just doesn't happen. O and H can't bond with N when a snow flake is forming on the way down. The chemistry just doesn't work that way.
It's a *little* more complicated than that. Snow & rain both "trap" nitrogen - that is, charged nitrogen-containing compounds like nitrates. It doesn't form new compounds with elemental nitrogen itself (unless there's lightning involved). Elemental nitrogen (N2) is absolutely useless to living organisms. You need nitrogen "fixed" into forms like nitrate for it to be useful. Lightning does that, as do certain bacteria in the roots of certain plants.
So yes, snow & rain do contribute nitrogen-containing compounds to your soil. I can't imagine that it's a great amount, certainly not compared to fertilizer, but it couldn't hurt, I guess. I also don't know why snow would be considered better than rain, in that regard. Maybe it sits there longer so there's more time for it to be absorbed by soil microbes before it runs off?