Is it good time to travel Guilin in early Jan and travelling cost(accommodation, food, entrance fee, etc) cheaper in Jan vs Aug?

Usually, April to October is the most favorable time to visit Guilin. January is not that cold. The average temperature is about 8C. Generally you may not miss something, because the weather is milder all the year round. It seldom rains. It also depends on where are you going. I think it is not the best time to see the Longji (Dragon Ridge) Terraces. If you can see the terrace in snow, it is also amazing. It is in the low season, accomodation is easy to find and cheaper. Hope it helps.