My rosemary spends its winters on the floor of the unheated greenhouse. At one time, I kept it on the basement floor, just where light from 1 window would fall on it during late afternoon. I think I lost nearly one-half the plants down there the last winter I tried that. And, it is rosemary plants, not plant, 'Dorie.
Perhaps you could grow one that is fairly large if it was in a massive container that you move in and out each year. My rosemary plants are all in 8" pots and I can carry one in each hand.
They are covered when temperatures drop more than about 10 below freezing - sometimes left for several days like that. I am reluctant to advise keeping them at room temperature thru the winter, just because I've never done that. Still, long before it seems like a good idea to put them outdoors again, the greenhouse furnace is turned on and things warm up in there. That's when new cuttings are made.
The horticultural advice seems to be to make cuttings in the fall. That may be okay, it just seems that when they are obviously beginning to grow that a cutting could be successful with a fair amount of the old growth taken.
They are stripped of needles and dipped in rooting hormone, then put in sterile potting soil. A whole flat of them can then be set where they don't really have any direct sun. They stay there for a couple of weeks and that seems important for the starts to grow some roots before they are moved into direct light.
All this works well. I haven't lost a plant in several years. No big rosemary plants, just lots of smaller ones . . .
Steve