some sort of snow rally tire designed to be studded, but don't put the studs in? a bit obscure, but at the 2009 Rally of Great Britain, some teams elected to run the P-Zero Corsa snows without the studs, due to the extreme wetness, and it worked out VERY well for those who did it on the first few stages and soon every team followed suit. that would get you great grip and the narrowness you're after.
alternately, look to Hoosier's dirt oval and vintage racing tires. they have DOT numbers and significant amounts of tread, granted Hoosier says that if they touch public roads you will crash and burn and die, but it could work.
failing those two (or perhaps should be ahead of those two...), look at what Coker Tire has to offer, that seems the most logical course of action, and then for rims, if you don't mind a VERY un-period look, rims designed for rally cars running snow/ice tires?