Burqin Sports & Outdoors

If you want to go on a horseback trek, you should get off the share-taxi at Jiadengyu, before the Hanas Lake park entrance. However it'll still cost 50 RMB/person from Burqin/Bu'erjin long-distance bus station.
At Jiadengyu you can find horses and grooms going to Hemu village, this'll take about a day.
Horses cost 150 RMB/day, grooms (mandatory) cost 200 RMB/day and you'll also have to pay for HIS horse which's another 150 RMB/day.
From Hemu village you could persuade the grooms to go on to Black Lake (a part of the Hanas Lake park) which's another 2 days (not sure) on horseback. This way you'll be able to evade the park admission fee.

Equipment: If you have a lot of luggage, I would recommend that you drop the stuff in Burqin before you go to Jiadengyu and Hanas Lake. Luggage storage is always available at long-distance bus stations in China. This is especially the case if you're going to do any horseback trekking, which starts at Jiadengyu. On your return, you should go directly by share-taxi from Hanas Lake to Burqin without stopping at Jiadengyu at all.