Is it possible to visit laoshan mountain in winter - January? What would be the best route?

Don’t worry, it’s still open in Jan.
Since there are many scenic areas in the mountain, according to that, I will recommend four classic routes to you:
1. Jufeng Peak line (which holds a 5,598 meters long sightseeing route.)
2. Jiushui line (the main attractions are Nine Lakes and Eighteen Pools.)
3. Taiqing Temple line (including Taiqing Temple, Mingxia Cave, Shangqing Temple, and Longtan Water fall.)
4. Taiping Temple line (you can enjoy Taiping Temple, Shizi Peak, and ‘Shou’ Peak.)