I understand your reasoning behind planting winter wheat for a winter cover. But, may I suggest something I found that was better?
I also used to do the same thing. Then I started planting crimson clover, and what a difference that made! The crimson clover is a great soil amendment, is a great green manure, and it also fixes nitrogen in the soil - just what corn and other vegetables need and want.
It isn't as hard to turn in as the winter wheat is, and it breaks down much easier too. BTW, if you do use crimson clover, it is something that has to be replanted year after year unlike white clover varieties that come back like a plague year after year.
Also, Jan will love the crimson flowers on the clover, and so will the honey bees.