Not quite.
What else does NY have living in this state that is capable of killing horses and climbing trees? BEARS.
I swear everyone who says there are mountain lions in NY KNOWS there are because of what someone else told them. Please, find me proof of their existence in NYS. A picture, with an article showing the picture or cat itself was confirmed by DEC as being in NY. I guarantee you, that you will not find one from the last 50-75 years. Mountain lions went extinct in the state over 100 years ago, and there are no more in the state.
And here is how I know you are wrong about DEC releasing a group of them onto public land. If they did that, the mountain lion would be a protected species in NYS, on the endangered species list for NYS, and there would be laws against killing them in NYS. None of that exists, therefore DEC will not CONFRIM the existance of mountain lions.