I am in New Mexico and I don't put them in the fridge. I put them in large bins outside once the 1st frost comes and then keep them moist all winter. It has been cold enough to give me a decent bounty of seedlings each Spring. So in New York they will get cold enough and may stay moist enough without you having to wet them. It's one way to do it but there are lots of methods and I am still learning. I know it's important though once the seeds are outside and in the ground not to let them dry out. And sometimes they don't come up till the 2nd year but if I don't get at least some sprouting the 1st year, I toss the seeds because I am not patient enough to wait years. I have heard stories of a seed sprouting a decade later(too nerve racking for me).
