I arrived in Kochkor just after 1 pm last Sunday and went to Shepard's Life. I just wanted to go to the lake and figure it out from there. I was by myself but was able to go a couple of hours later with one of the Song Kol families in town for shopping for 1300 som one way (1½ hr trip). Sleeping in a yurt with full board is 1000 som/night. Booked 2 nights and the one way ride. Thought I might be able to do the reverse horse trek once I got to the lake but it is difficult to arrange there because the guide heads straight back after dropping off the group ~5 pm.
Taxis in town ask 3000 som to the lake (up to 3 pax, might be able to bargain) but that is round trip as you have to pay for their return. The agencies charge 3200 som for up to 4 pax + ~200 som/night if you want the driver to wait up there with you before returning.
First day was nasty - cold, rain, wind, intermittent sun. Second day was much nicer. While wandering around looking for a ride I was invited into a a family's yurt (not affiliated with any tour operator) for vodka, kimis, then outside for the goat slaughter. Interesting. Later cadged a lift to Kochkor with an Austrian family departing for Bishkek the following morning.
I met many people who did the horse trek and they all spoke highly of it. Standard trip seemed to be 1 night at a yurt in the woods, second night in a yurt at the lake, depart back to Kochkor in the morning.