Cactus don't need much nutrient but roses do. If you want to use the cacti soil, add some liquid fertilizer for house plants with it. Don't forget to mist it with a sprayer just one spritz a day. Most homes are very dry and warm. and that will dry out the rose and kill it.

It will last best as it is now until planting outside in spring. I would not up-pot it at this time. With the miserable rose growing conditions inside the average home, the rose will already be pretty stressed. It could die from more stress.

You will probably find, come spring planting, that there are several plants jammed together in that little pot. You can separate them at that time if so.

Putting the separated roses in individual, appropriately sized pots, and grown that way for 8-12 weeks, then planted in ground would give better results than planting them right into the ground come spring . They will be much huskier after their potted period is over, than if directly planted into the ground right when it's safe to do so in spring.

Use a good, general purpose potting mix, not cactus mix.

Those gift miniature roses are usually toss out, throw away plants, once done blooming. They are primarily greenhouse, disease prone plants that are meant to be pretty for a couple weeks, then the show's over. You may have success with them, but I can almost guarantee you will face a challenge growing them successfully.

Moses

Moses’ general caution about success with gift mini roses should not deter you. Six years ago I picked up 3 at a NJ supermarket July4th special. $2 each. That Thanksgiving, I popped them into shallow holes in a neglected part of the garden amoung astilbes and coral bells.

Two were alive the following spring, and today one is alive and thriving. One of my best performers as regards foliage health and flower production. I laugh every time I see it. Receives zero care aside from pruning. About a foot tall, tops. They were grown by Aldershot greenhouses in Canada. I recollect they were Kordanas, or Poulsen related. The thriving one is dark red.

If it was my rose I would repot with the right soil in to a slightly larger pot. Get it out of the warm house. If you have a garage that would work. If not, take the small pot and place it in to a larger pot and fill between the two pots with mulch or towels

Wrap the larger pot with burlap or more towels.

It is a pain but it can be done. I did it last year with two Gigis. Good luck!