One of the most popular species hunted for in NY state are the whitetail deer. They can be found virtually over the entire state. The hunting season normally starts Sept. 27th and ends first week of December.
Weapons: In the northern counties a rifle is the preferred weapon. Calibers run from a .243 up to the popular 30-06. Many of these counties are sparsely populated and rifles are allowed. In the southern counties shotguns are widely used. Ranging from the small kick of the 20 gauge to the 12 gauge, these have killed many deer.
Weather:The weather in NY state can range from a ocassional day in the eighties to a day down near zero. The season last for the entire autumn time line. My suggestion would be to wear layers of clothing so you may add or subtract them as needed. Florescent Orange is not a mandatory item but is highly recommended.
Safety Tip: If you go to the northern counties I would suggest a compass, good hunting knife and a emergency kit with matches. In many spots you can get turned around and end up spending the night in the woods.