Blue Mountain Reservation
Region: Hudson Valley
Blue Mountain Reservation is located in Peekskill, NY and is a 1,500+ acre park of more than 20 miles of trails through rolling hills, easy but enjoyable climbs, and deeply-wooded tree cover. It's great for hiking, running, snowshoeing and mountain biking. I spent a few hours making the trek through the snow-covered forest on the Blue Mountain summit trail. Once I reached the summit, which is an easy and very small climb (only 680 ft. in elevation) I found a decent lookout area in view of the Hudson River. From the summit I travelled down the Limbo trail, met up with the Crossover, took that towards the Yang trail and made my way back to the main road that leads to the Trail Lodge. The Westchester County Government's website has a great trail map you can find here. In addition to the summit of Blue Mountain, there is also (an even smaller) peak you can summit towards the south-eastern end of the park called Spitzenberg Mountain.
This winter I've done a little more hiking in the snow with hiking boots and Yaktrax (basically winter cleats that wrap wrong your boot) as opposed to snow shoes and I've really learned to enjoy the extra effort it requires and the feeling of being out in the cold working through the wilderness. It has a bit of a different "wild" feel to it, plus the views can be quite picturesque with snow-covered terrain. If you're interested in doing a hike in the snow, I would highly suggest BMR for a first time out given the gradual incline of the trials. I would still suggest getting some Yaktrax or other cleat-type attachments for your hiking boots, though.
Coming from the city, this is a very simple trip up the east-of-the-river Metro-North line to the Peekskill stop. From there, I think the best and easiest way is to call an Uber to bring you over to BMR.