an unheated greenhouse is basically a cold frame you can walk in. If you need to keep things a little warmer, there are a few things you can do.
1: try putting a second layer of plastic or frost cloth over the plants INSIDE the greenhouse. According to Elliot Coleman, every layer of frost protection increases your zone by 1.
2. if you have room, place barrels of water in the greenhouse, near the most susceptible plants (metal works best, but even plastic will help) As the temperature drops and the water begins to freeze, it releases energy in the form of HEAT. This is why watering your plants before a frost can sometimes help the plants in the field.
3. if you have access to fresh manure- put a bunch of it in the greenhouse. As it rots, it will release heat. This was the origin of the "Hot Box" as opposed to the Cold Frame.
Last but not least, choose to grow cold hardy plants, and give up on the idea of fresh tomatoes at Christmas, lol, unless you can grow them inside your heated house.
In your zone, and indeed in mine as well (Zone 6), plants don't actually grow during the winter months- probably because there simply isn't enough sunlight. But if you start them early enough to get some good size on them before the short days, they will go into a sort of stasis- you can harvest them, but they won't put on much growth. Your perennials might do just fine in the greenhouse (they won't need a lot of water, but you still need to check that at least occasionally- I lost my rosemary because I forgot to check), Lettuce may do ok. The best greens would be the really hardy ones like endive and chicory, and especially mache, which is the most cold hardy green I know of. In fact, it won't even germinate in warm weather, lol. I didn't start things early enough this year with everything else going on, but things like chard and kale and such would probably do well too.