
Let's assume that the option of putting the rose in the ground, pot and all, is not available. If you have a garage around 40 F that is a possibility. You will have to gently water the plant so the soil doesn't completely dry out. This is critical; it is drying winter winds that kill hardy plants more than cold temperatures. Roses continue to need water even when dormant. If roots are allowed to dry out, winter kill is likely. Since container plants are no longer high on our To Do list once winter hits, put watering on your calendar! (every 2-4 weeks) A balcony has higher winds than ground level. If your rose has to stay on the balcony, wrap it with burlap or heavy cotton (leave a place for watering) and put straw, chopped leaves or mulch 6 inches high in the pot. Around the base, place bags of leaves or partial bales of straw to keep the roots from going through freeze and thaw cycles. Or, get a large cardboard box that fits over the rose and pot (or make a chickenwire cage) and fill it with chopped leaves or straw. It should have at least 6 inches clearance at the base to allow enough insulation. Snow is also a great insulator. Interested in making an igloo for your rose? If not, go ahead and mound snow outside your other insulating materials. When I search "winterizing balcony roses" I see there are products for sale, e.g. a mini tent for your rose. This will help with winds but doesn't provide insulation itself. A plant protector bag may be more appealing than the cardboard box I suggested.
https://www.gardeningknowhow.com/special/urban/overwintering-balcony-gardens.htm
https://www.gardeningknowhow.com/ornamental/flowers/roses/roses-winter-care.htm