I have never been on the ice up there, but does Kab really have much for current? I could be wrong, but I don’t think there is enough anyway to really affect anything until you start getting near The Ash River, Nam, and Kettle. There aren’t much for rivers actually flowing through the main body of Kab.
I know the Park Service plows a road between the two visitor centers. There is also a marked snowmobile trail they maintain as well. I’d assume stay near them and you should be fine as well.
Hopefully someone knows a little more as I’ve been pondering a trip up there as well.