Raspberries Overwinter in Greenhouse

I found a wild red raspberry patch while kayaking last month. I brought home some cuttings and now have about thirty 4-inch stems putting out leaves in my wife's rooter/cloner gizmo. Once they put out healthy roots, we'll transplant them to potting soil to develop further.
We're in central Maryland, north of Baltimore, so there isn't much time before the cold and frost hit. I was thinking about just putting them into the greenhouse over the winter, which should allow them to keep growing and developing until spring, when I'll plant them outside in a permanent bed.
Would there be any problem with keeping them "awake" all winter instead of letting them go dormant?
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