February is going to be cold to very cold all over Yunnan. The 5-day time frame works with going to the Lijiang area and TLG, though if you want to do the overnight hike, you'll be limiting your options around Lijiang itself--but that can be sorted out in real-time once you see the weather. Usually TLG is not subject to much winter snow, but Lijiang could be and definitely Jade Dragon Snow Mountain. You may find that access to the top area of the mountain itself would be limited by weather or cable car not operating. You need to consider staying in a place with good heat. In Lijiang (or sidekick Shuhe) consider staying in New Town at a more modern place rather than a quaint old-town guesthouse that has nothing better than electric quilts and limited hot water.

Not sure if flights into Lijiang are going to be running cheaper then, nor sure about possible disruptions due to weather. The schedule will be cut back for sure unless you're traveling early enough in Feb to get into the post-CNY holiday travel period. But even on the 5 day time frame, flying to Kunming, taking the overnight train up to Lijiang then doing same on the reverse is possible and likely would save a goodly amount of cash.

Another possibility is Kunming - Jianshui - Yuanyang area. Terraces will be flooded and very scenic then. Works with your time frame and wouldn't be as expensive. Weather still going to be chilly but not like upland Lijiang.

I'm still not completely sold that Yunnan is the best use of your 5 days though. Any other things on the wish list? Is natural scenery the trip focus?