Yep. I do both. But you need to watch the temperatures inside the cold frame. They can overheat quickly, so if I were you, I'd make sure there's a couple of holes in the covering just to keep it from getting too warm, especially with a clear covering.

At 45 degrees, my hoophouse gets up to 80 inside. That's using a 6mil "clear" plastic that transmits only about 85% of the light that passes through it. I haven't calculated that, just from what I've been reading on the greenhouse forum.