Onions definitely, the hardier greens, such as kale and collars, possibly some lettuces, cabbages, chard, some of the Asian and European grens like mustards, corn salad/mache, leeks, winter radishes, beets, turnips, rutabagas, certain herbs like parsley or chives.

How long and how well things will survive will depend on just how severe your weather is, and how well they are sheltered. You may have even greater success by mulching the crops heavily with straw right in the hoop house/cold frame.

Still in good health in my garden, wrapped in several layers of row covers, are winter lettuces, komatsuma, red mustard, escarole, arugula, and savoy cabbages. Under hay are turnips, beets and carrots. And standing tall and proud with no covers at all is the Winterbor kale. The cabbage was started in June and set out in early July, the greens mostly in late August and early Sept. and the kale, beets and carrots in July, the turnips in August. A late Sept. planting of spinach has yielded plenty for salads and will overwinter and begin really producing in March.

I won't have to start on the frozen veggies until January, and by the time I'm getting tired of them, the spinach will be kicking in.

Mine were going strong a week ago, but now they're under a foot and a half of snow. Hmm. I like the hoop house idea ....

This was my first year gardening and pulled some fresh carrots for our Christmas Dinner. They grew slower than I thought they would, but I ended up with some nice ones.
My mustard greens, broccoli, and lettuce are still growing, although slower with the cold.
With my climate, I could probably keep winter veggies going all winter. We've had some nights down in the mid to upper 20's. I also mulch heavily though and have raised beds.

Pete

The garden grows slower with less sunlight but since the Solstice has passed things should speed up a bit.

I don't really need it around here, but I have read about how gardeners in cold places like New York would build cold frames and put a really thick layer of manure under the soil so the heat from the composting would warm up their cold frames. The article was written in the late 18th century and there seemed to be a LOT of manure around. If you have a horse stable nearby, maybe you could try the same method.