I lived in South Dakota for almost 20 years. While there I explored the other central states such as Kansas up to North Dakota. Pheasant are indeed a winter - hardy bird. Up until the 80's they were common in the Northeast too. Not so much today. You need to be realistic and most people are not about this. Although SD does not have a state-sponsored pheasant stocking program, the commercial preserves stock around a half a million (500,000) every year, and they have done so for decades. The closest to that number is Pennsylvania which stocks 225,000 a year. Indeed there is a huge population of wild (breeding) pheasant in SD, but slot of the birds you see, and despite what the experts say, many members of the wild, breeding population, owe their existence to stocking.
If you are interested in traveling to New York, my section of the state pheasant hunting occurs during the month of October. Send me a message. A 3 day vacation license is avail. for nonresidents. You might also look into quota hunts in the stocking states. The hassle of "waiting your turn" is worth it. I believe in hunting local, but those who are able to travel should explore some opportunities, this is one.