i dunno, if there's one thing that we know about roose bolton, it's that he's cautious as hell - i very much doubt he trusts littlefinger at all and it's an incredibly risky move for him to take in sansa, much less not alerting cersei of it when stannis is knocking on his door and he needs all the support he can get right now
Roose still was pretty calculating in this- it was either take in a Stark to give himself more legitimacy in the North and disrupt the Lannisters or keep the situation with other Northern families the shaky way it is and keep the Lannisters where they are. Really a crapshoot either way, and given that people like House Karstark are going to be more helpful in immediately coming to aid when Stannis attacks, he chose this.
littlefinger also has no reason to believe that roose isn't loyal to cersei, and given the amount of effort he put into secretly sneaking Sansa out of king's landing, it's hard to understand why he'd just hand sansa over to roose
That's why he went to Cersei in the first place instead of blowing her off. Cersei didn't even know where he was, so she couldn't exactly punish him for not meeting her. Roose may still be loyal, but Cersei now (probably, assuming she wasn't playing dumb for Littlefinger) distrusts Roose, which is even better when you think about it. As mentioned before, Roose can only hurt Sansa so much- she's there to placate the Northerners, giving her back to the Lannisters will cause a full-scale uprising right then and there.
isn't a better plan for littlefinger to head to the wall and try to win stannis baratheon's support?
IMO, Petyr has a much better chance of convincing Cersei of one more in a looooong string of half-truths and lies than convincing Stannis to trust him and ally with him. Safer bet for him.
littlefinger's plan doesn't actively work out for him in most scenarios
* if stannis and roose fight and then the lannisters come in to clean up, he loses sansa (and given how the show has portrayed him as absolutely obsessive over both catelyn and sansa, he'd probably rather avoid this)
* if stannis wins then littlefinger is actively screwed regardless of whether he's allied with the boltons or with the lannisters
* if roose bolton stays alive and ramsey bolton eventually is named warden of the north, neither sansa or littlefinger actually gain any power???
If his gambits with Sansa and Cersei go the way it's planned:
If Stannis wins and stays, Sansa is given power (unless Jon decides to change his mind, but is unlikely) and Littlefinger gets power that way. Stannis will definitely not hurt Sansa.
If Stannis wins, but is then beaten by the Lannisters, Lannisters gain control of the North and he is rewarded for telling them to go there.
If Roose wins and stays, this is the only scenario where Littlefinger really loses, but even in Game of Thrones where evil wins 99% of the time, the Boltons being able to resist Stannis, the Lannisters, and (most likely) the other major Northern families is quite unlikely.
If Roose wins, but is then beaten by the Lannisters that he got to distrust the Boltons, same thing would happen if it was Stannis.
Plus, if the Lannisters lose, that weakens their position in the South, creating a small but noticable power vacuum that someone with the Knights of the Vale behind them would be able to fill....
