The dome idea seems to be a bit of over kill to me but your two zones colder than I am. I would think it may work best if you can incorporate a flip top to removable top about 1/3 of it's top. From time to time and especially on warmer temp days the mini will still need some form of good circulating air and you can flip open the top on them better days and replace it on colder ice stromy days.

I prune minis down to about 1 - 1 1/2 feet in height and then bury em up to 6-8 inches in hay and fallen leaves. This idea will save you from having to walk in some deep snows during the winter months ahead and it will allow for good air without added efforts.
Best of luck
Wes

As Weslety says, when using styrofoam cones or domes, be sure you have a way to provide ventilation on warmer days. Otherwise the buildup of heat and humidity inside the cone will be very bad for the rose.

Thanks. I may just cut off the top of the dome and use it as a way to keep the fallen leaves around the rosebush. Might even poke some holes in the sides for air flow. If we get a lot of snow, it will soon be covered anyway.

Minis are on their own roots and are hardy. I don't protect mine at all, unless some leaves blow in on them.