I am becoming a big fan of Schwalbe tires, The Big Apples are grippy, the Supremes are better. In the Winter, Ice Spiker Pros rock! They allow me to ride where I can't walk! If you get the BAs, try running them down to 35PSI or even lower, there is little loss in speed, but marked improvement in ride. The Supremes, maybe 40?
I often shortcut through a patch of woodland, the BAs handle wet grass quite well, even thin mud with care.