Most routes in the Dales are all-weather but the bit above Foxup is one of the exceptions.
There’s a Stainforth loop in the Vertebrate Dales South book that is reasonably all weather: Stainforth -> up road towards Halton Gill -> BW down to Helwith Bridge -> BW up to Penyghent -> back to Halton Gill rd -> BW down to Litton (HB to here is the opposite direction to the lower line on the OP’s map) -> road to Arncliffe Cote > BW over to Malham tarn (first bit can be muddy) -> BW to pick up Settle loop -> follow SL back to Stainforth.
On the OP’s indicated route I wouldn’t head up from Litton to Dawson Close (5 -6), the first Km or so will just be pushing.