You are not understanding the power snow has on corn! I just wrote this up on pirate island but I'll do it here too for kicks.
Tough call. It is not a very good feeling to still have hundreds of acres of corn out in the field at the new year. We've experienced this many times and it is just no fun. If you are going to keep corn out all winter, you have to be very smart about it, you have to aggressively scout your fields to find the varieties that are standing very well. If the stalks are breaking before the snow flies you are going to end up using a bean head in the spring to harvest moldy mud covered corn.
This is from 2006 in February. As you can see there is a tremendous amount of damage to the corn and the yield loss was close to 20%.
It can be very spotty though,
I don't have any pics before I sprayed the beans, but there was a lot of volunteer corn in the beans the following year. Fortunately it was Roundup ready beans and not roundup ready corn!
Also, just because you think the ground is frozen, doesn't mean it is frozen enough.
My personal opinion is that it is better to mud off the crop, ESPECIALLY soybeans, and deal with the aftermath of the mud instead of wrecking your equipment in the winter. Not only do you get stuck in the snow and icy crap in the winter, threshing frozen grain is like running gravel through your machine, you do excess wear to everything.
Ok, lets say you don't get done and you leave excellent standing corn out in the field and it snows a LOT.
Notice where the cobs are, right at snow level. The loss from small animals is astronomical! The geese just walk up and down the rows eating at will. Same with the deer. Same with the coons.
Not only that, all that snow when it begins to melt, melts from the top down, but also the bottom up. So you end up with caves. Eventually the ice pack falls, and it takes the corn frozen in the middle of it down with it.
Trust me, as bad as those ruts might look, you are going to make the same ruts in the spring getting half the crop.
Just a different point of view for you to think about.
Warren