I have a friend who watches soil temp a fair bit. I know at least in W ND, the soil temp was above freezing when the bigger snow systems arrived. Now the snow is like an insulating blanket and unless we drop into the deep freeze for several extended periods over the winter, the frost won't be as deep and much of the snow will soak in as it melts rather than running off.
The other unknown of course is the speed of the spring thaw. If we get some of that out of the ordinary really warm days very early the snow may melt too fast to soak in even with reasonably shallow frost depths.