Neoprene chest waders and felt soles. Wading staff helpful. Anglers can wade much of the river, especially the upper part, but crossing can be dangerous due to the strong flow and dropoffs. Also, the rocks are covered in moss and very slippery, so wear felt soles. The river is a constant 42 degrees so neoprene waders are a must.
Winter storms blow in unexpectedly and fiercely.
Bring harsh weather gear. The San Juan and Green Rivers are arguably the top winter trout fisheries in the West. I recommend hiring a guide if you've never fished the San Juan before, since the techniques the guides and locals employ can make all the difference in catching twenty big trout or talking about the one fish that got away. The only way to float the river is in a boat, usually a MacKenzie boat, no motors. No float tubes.