In my opinion, the season is just timed wrong, we should bowhunt from mid october (like we do now) until mid December, bring the guns out from mid December till mid February.
And make Turkey season start on March 1st and end mid May!
It isn't timed wrong, our calendar is wrong.
We've miscalculated the actual length of a year.
By using leap years, over the centuries, our months have lapped our seasonal climate changes.
This slight miscalculation, multiplied by the centuries, has given us summer weather in December and caused our deer rut in the spring.