Why didn't the powerful Han Dynasty immigrate to Northeast China and Korea?

There are immigrants in Korea, namely Lelang County, Xuantu County, Fan Zhen County and Lintun County. But there is no northeast anymore, because even Liaodong is already a bitter and cold place, and it is impossible to live in the northeast in winter. After all, there was no cotton at that time. For ordinary people, they can't afford to wear fur, no cotton-padded jacket, no down jacket, air leakage in the house and no charcoal burning. How can they live in the weather of MINUS ten degrees?