Very limited experience of the area...walked nearby earlier this year when I was doing parts of the Leeds/ Liverpool canal. Really pleasant part of the world and I wouldn’t see any real problem in walking that sort of terrain in winter, barring exceptional conditions.
I am interested in doing the Herriot Way myself sometime, and did some very low key “research”, and quickly found that one of local hotels/ B and B’s did a package, where they take you out to start of each day, collect you at end of day..then take you out next day to where you finished day before. So possible to just stay in same B and B to do the Way.
Call me soft...but that’s the way I’d do it in winter.