Just a thought, but if you want to keep the population up and are worried about the winter kill, the best thing you can do is get out there & kill roosters.
In SD we figured out that the roosters push hens off of feed in bad weather. Winter 1 hens die off. Spring = limited hatch. Takes 3 or 4 years at best to get the population back up. You just about can't hurt the population by killing roosters.
Congrats on the hunt & thanks for sharing.
God Bless,