Since you are in NY, you may want to join Views from the Top, a NE/NY hiking forum. There are plenty of very experienced NE hikers on the site (I belong, but live in CA) and what to carry on day hikes gets discussed fairly regularly.

For me, if I am day hiking in winter (with snow on the ground) I carry enough to stay overnight. That includes a sleeping bag, extra clothes, stove, food, light bivy sack and my Voile Mini shovel, plus the usual first aid kit, headlight or flashlight, map, GPS etc. I know that seems like overkill, but a lot of VFTT members do the same. I'd also have snowshoes.