During the past 20 years or so, advocates of season extension, such as Eliot Coleman, have demonstrated that some vegetables can be grown right through the depths of even northern winters with inexpensive and unheated buildings called hoophouses. These are simple structures of steel "hoops"--steel tubing bent into an arch shape and anchored to the ground--covered with a single or double layer of greenhouse plastic.
Extending the Season
Consider fitting a second layer of plastic over the hoophouse to create a layer of insulating air between that and the inside plastic with a small fan. This will slightly diminish light transmission, but not to a point that will interfere with your plants' need for light. What it will do is greatly increase the ability of the hoophouse to maintain more stable temperatures.
Make sure the soil inside the hoophouse is well amended with good compost, has a complete range of plant nutrients, and has a pH (acid-alkaline balance) of 6.5 to 6.8. Your local County Cooperative Extension office (listed in the phone book) can help you arrange soil testing.
Plant seeds or transplants of crops that you intend to over-winter no later than early October. In cold weather, with decreased daylight hours, protected plants will survive, but they will not grow. You have to get them all well established before really cold weather sets in.
Choose crops that don't mind cold weather, such as 'Winter Density' lettuce, 'Spargo' spinach, 'Astro' arugula, kale, and several Asian greens such as mizuna, tatsoi, and Tokyo bekana. In the ground, carrots, beets, and daikon radish will survive if heavily mulched.
Construct "mini-tunnels" inside the hoophouse, using wire hoops and row cover fabric. Under this double layer of protection--the hoophouse plastic, and the row cover fabric--your plants will effectively experience the climate of a USDA zone two zones south of your location. You might be in New York state, but your plants will think they are in Florida! Plants that look as if they have been terminally "frosted" in the early morning will perk right up and look just fine by noon.