what is Guilin like in january?

January there is coldest time for that place. The temperature difference is big with a average temperature at about 7-8C. It is cold and humid without. No heaters in the rooms.
It is the not the peak time of traveling, so the fees will be lower. If you want to go at that time, you need to prepare the thick coat and sweaters.
During that month, you can take a small raft to enjoy the beauty of Li River instead of the cruise or hiking, which are more interesting.
Anyway, if you can keep warm, it is still not bad to go there in January.