I actually guide on the San Juan and it turned over on Dec 16th if I remember right. It will turn over again in the spring, it is temperature oriented. The extremely mossy phase of the turn over is past for now and has been for a while, although it's still very murky it's fishing very good.
As far as flies go all the usual suspects are still catching fish. Right now the hatches are much much smaller in intensity and length than during the warmer weather but I'm still catching fish on emergers, KF Flashers, RS2's, Top Secret Midge etc. It totally depends on the area of water and the hatch. In other areas a Chamois leech, Bunny leech (darker color), Streamers, red annelids and cream UFO's are the best approach. Some people I'm sure are having luck with other things as well and probably swear by them, this is just what has been working for me at this time.
They stocked it recently and the biggest problem is keeping the smaller fish off and finding the big ones. The big ones are still there and still feeding, I've actually taken to ignoring the big obvious strikes, unless they hook themselves, and only setting on the very subtle takes. Not always but this usually results in a bigger fish.
Right now is actually an awesome time to be fishing the Juan, waaaaay less people to contend with and the fish don't quit biting due to the color of the water. Just watch the projected forecast and wait for a warmer day and no or light wind. I think you'll be glad you came. The Sportsmans is the only place open for food right now and they are currently closed on Sunday and Monday.
JH
Trout Junky