I don't think I would trust your weather (or mine!) in springtime. This year, the second half of April was beautiful, so I planted tomatoes and cucumbers in the unheated greenhouse, a solid building attached to the house, with plastic sheet over the front end. First two weeks of May, winter came back and took out half my young plants. A mini-tent - plastic sheet hastily stapled over the bins - helped, but I had to lug all the peppers and some of the tomatoes back into the heated part.
Bottom line: It's a worth a shot, but make sure you hold back spare seedlings, just in case.
