S2LZ4, I've met a few rose lovers from Z4 and I'm always amazed at the ingenuity they have in dealing with cold winters. One couple grows only minis. On halloween they move all the minis into their dark basement. Then (not sure when) in spring they set them out again. In Ottowa, I understand that it is not uncommon to dig a long trench for a climbing rose, and to bury the canes for the winter in six or ten inches of soil.
I love the idea of an insulated box with its own heat source, namely compost. I think if I were doing your project, I would make a heavy wooden box lined with an inch or two of styrofoam insulation, preferably with aluminum foil facing inside. I would put wood shavings/sawdust in a pile around the plant, then place the horsey doo further away, but inside the box. Then, hopefully, in spring the material in the box has decomposed into compost that sits on top of the soil and enriches the soil. This has the advantage of not requiring that you know how deep the roots go.
I would be tempted to paint the box a dark color, so that it heats up during the day; but if it gets too warm in there, the rose will break dormancy, try to grow, and freeze. So whatever color you do or do not paint the box, you might consider monitoring the temperature at three pm or so and make sure it's not too high. Not sure how high is too high, but you probably don't want it to get above 55F.
