I’d pull the fuse for the stereo, and also the fuse for the cigarette lighter or accessory circuit that is powering the second power input, the one that is on all the time on the stereo. I guess you’ll know when you have the right one if the lights go out. Then replace the accessory fuse and stereo fuse in that order. Now see if your attempt to reset it worked. If you’re lucky, that’s all it needed.
If not, it will likely be cheaper to junk it and get a newer and better stereo than to try to fix this one. It sounds like more of a malfunction than something caused by the cold.