I don't cut them down. I cut the scapes off after they bloom, but not down at the ground level. I've heard that keeping them ground level helps avoid rot. Those scapes are hollow; they can hold water. So if they are real low, they can help promote rot in the spring when the snow is gone.
I allow the oak leaves to cover the hostas over the winter. Somewhwere I read to do that, too, to help keep the hostas from popping up out of the dirt. At this point none of my hostas are going to hop anywhere; they weigh a ton. Anyway, in early spring I rake away the fallen leaves, pull out the rest of the scapes, and clean up everything. My timing is usually bad. If I could get to this before the pips start coming up, that would be perfect. As they rise is bad, because I can't see them and step on the poor babies. So I usually wait until I can find the pips, then very carefully pull away the leaves and scapes and rake where the rake will fit. It takes me weeks to get all the leaves up. Lots of oaks surrounding the property, lots of hostas, lots of wind.
