cmeg, I think that you should keep them in the cold frame, and keep them as cool as possible. Meaning in the shade and mulched. You could wind up killing them by moving them in and out of the warm sun and cold frame. Trees need to go dormant, and stay dormant in the winter. This has been problematic this year, as it's been too warm for much of the winter so far.
But you should keep them as much as you can in a cold sunless area for the rest of the winter. If they wake up, and start to bud, then the next cold snap will kill them. Open the cold frame on the warmer days.... Trees don't need light when they are dormant btw.
This will also save you some trudging around with your trees at any rate!