Was the LF arc with the starks all let of thier plan?
We're the stark girls playing little finger all along by inviting an opportunity for him to sow discord between them?
What was LF's end game in mucking about winter fell?
I have no idea why Llittlefinger was hanging around Winterfell doing nothing, and apparently creating trouble just for something to do. By all rights he should have headed south to "save the Riverlands", that is, take advantage of the power vacuum created by the massacre of the Freys. Sure, he's waiting for either Cersei or Danerys to win the war so he can deal with the winner, but going to the Riverlands would have allowed him to deal from a position of strength, it would have put him in control of the northern half of Westeros.
Instead, he just hung around Winterfell, probably intending to win Sansa over, but that just doesn't work on girls who've spent long periods of time being raped and tortured and he should know that. I suppose they meant there to be some terribly irony about this soulless sociopath more or less dying for love, but I don't think it really came off that way.