Hi Summit. It sounds like your Dracaeana got frost bit, but now that it's in a warm location, leaves shouldn't be browning. Was it brown or more gray? Frostbitten leaves look more gray than brown.
How cold was it, and how long had your plant been outdoors?
When leaves brown, are they crispy or soft? Also, does the entire leaf or edges brown?
Is your JC sitting next to a heating device? Vent, etc?
You can either air-layer or cut the main trunk back from the base, near soil line, or a few inches from soil. Root the top, either by cutting sections or the whole trunk. Rooting can be done in water or soil. The bottom will send out new growth. The only problem is, there's no guarantee, (if your plant is a JC) it'll grow upward. In other words, it probably will not grow erect. Instead growth will sprout from the sides. It depends on the plant.
How tall is your Dracanea? Do you have a picture? Toni

I don't have a picture unfortunately. It is about three feet tall and the leaves that die turn brown and are still soft not crispy. They don't look grey at all. They kindof yellow then brown but don't fall off. It got really cold, like 10 degrees it was the middle of winter when we moved and it had to go outside. I did cover it though. However, my fiance loaded a bunch of firewood and left the door open for a long time and our house got really cold. All my plants suffered when that happened so it may have gotten too cold a second time. The brown starts at the tips of the leaves then just keeps going. It is not next to a heating device but it is next to a window which I think is pretty cold. We don't have a lot of light in our condo so I try to keep our plants next to our one big window. Hope this information is helpful. Thanks for your help I really appreciate it.

Hi Summit. I had a similar problem this winter. I bought a Striped Dracaena at the grocery store. It was out no longer than 3 minutes. From door to a warm car. That night the temp was about 3F. By the time we got home, most leaves were frostbitten. They had a gray-brown color, and felt soft. I clipped them off, thankfully new growth is normal. IMO most if not all Dracaenas are cold sensitive, so temps before 32F will freeze a plant in minutes.
How cold do you think the window gets? Did you ever check the temp there?
Unless your window was opened, or leaks air, even on the coldest nights, a plant shouldn't frost indoors. (My front windows leak air, we place towels underneath all winter, sthere were times plants frosted)
If seeping cold air isn't the problem then it's possible Dracaena roots iced over.
Do you keep soil wet? They only need water when soil dries. Also, if an area gets cold at night, it's best watering in the morning, so a newly watered plant doesn't sit overnight in the cold. I lost a Sago Palm and Pachypodium/Madagascar Palm Cactus watering at night, because the area leaked cold air.
If leaves are yellowing, there's a chance you're overwatering. Unfortunately, marred foliage will not turn green, nor, on a JC will new leaves grow.
So, you have two options. Either let the JC grow as is, (palm-like) or cut in 3" sections, and root. What do you think you'll do?
One more thing. This probably isn't the cause, but have you checked for plant bugs? Toni