I'm a bit late with this report, but I was able to test Paul's suggestion of surgical gloves worn under fingerless wool gloves and also using a small tungsten bead on a size 18 fly (killer bug). Both worked very nicely. The rubber gloves did keep my hands dry and sufficiently protected from the brisk early January breeze (although it wasn't below freezing). The very small 5/64" tungsten bead did not cause casting to turn into a chuck and duck.
The stream was pretty small and not very deep, but the fish were holding in the slower, deeper pools. Having at least a little weight helped, I think, as there were not always places where I could cast far enough above the expected lie to allow an unweighted fly to sink to the right depth. Also, the new 9' 3" Tenkara USA Iwana I was using, with a similarly short line, does not allow for casts to be any longer than absolutely necessary.
I think adding a little weight, particularly for wintertime fishing, is one area where American tenkara will diverge from it's Japanese roots. I want to add as little weight as possible, though, because I really don't want to lose the effortless fluidity of the casting. I think tankara anglers can take a tip from French nymphers and use small, dense, thin flies that sink quickly without requiring a lot of added weight.