I have never hunted Carter's Pond but I have done well at the Wildlife Management Areas in other places (not always in Saratoga County). If you are into waterfowl a lot of people hunt fish creek, which is a part of saratoga lake.
If you want spots close to Saratoga I recommend heading out West 15+ miles. I had good luck out there knocking on doors. I was only asking to hunt small game, a lot of farmers are happy to give access. Some of them may want you to come shoot groundhogs over the summer, which can cause some serious damage to their tractors.
I would give some names and numbers, but I stopped hunting out there and lost contact. I just dressed respectably and knocked on some doors, offering some free labor in exchange for hunting access. It wasn't too hard to find good land to hunt. Many farmers didn't care about the free labor, they just wanted to know who was going to be on their land.
I have also done very well in the Southern and Central regions of the Adirondacks, although it did take 1-2 years to find some of the more productive areas on tracts of public land.
I great up in eastern PA and I have found the hunting opportunities to be much better here in NY.