I don’t think it will survive indoors. It is too dry. I have had no success over several years indoors.
I am not sure what zone you are in. I am in zone 5-6. Mine is planted out doors in a sheltered spot behind the house to see if that will work.
I have a cement retaining wall in back of the bed, and Milk Jugs of water on the sides(works better if painted black). It faces south west. I covered it with a row cover which is good down to 28 degrees. This lets in a good deal of sun and moisture, so I don’t have to adjust it on a daily basis.
As the weather gets colder, I put a second layer of row cover on it, and cover it with straw as needed. Sometimes I cover it with a thin, old styrofoam matteress about 3/4 inch thick. If I have an unusually nice day, I roll the cover back and let the full sun in, water etc.
This has worked well for my winter garden in the past. I have grown lettuce and a few other crops year round this way. I am hoping it will work for the rosemary.
I have also been giving some thought as to how to rig up a light bulb in case we ever get a colder than usual winter. Course, I would really like a green house, but no way to afford it, so I just improvise with what I have.
If you get sunny days, and have a bunch of rocks, these can be stacked around it with some sort of cover that lets in the sun. Plastic might have to be adjusted to avoid too much heat. The rocks will absorb the heat in the daytime, and release it at night.
I'm in 8a, nominally, but my microclimate on the north of the property can get much colder than the rest of the property.
/johnny