I think his plan makes some sense. I don't think it's the best course of action for Littlefinger, but then again in the show Littlefinger has taken plenty of unnecessary risks (telling Cersei he knows about her incest while alone with her and her guards being a particular standout).

Why is he acting now?

• His power in the Eyrie only lasts as long as he can influence Robin
• Winter is approaching, and soon the North could become too treacherous to travel across
• Tywin is dead and the Tyrells are taking control of King's Landing, meaning Cersei's attention is focused there
• With Roose and Stannis in the North, the power balance is uncertain
• If he waits, the opportunity could be lost because Roose could marry Ramsay to a different Northern lord, or Stannis could win and appoint his own Warden of the North

Why marry Sansa to Ramsay Bolton?

• If the Boltons win, Sansa may still be able to influence Ramsay
• If Stannis wins, he's unlikely to remove Sansa from Winterfell because this would anger the Northern lords
• Littlefinger ultimately wants revenge against the Boltons for their role in murdering Catelyn, and this gives him an opportunity to exact that revenge

Why not send Sansa to Stannis?

• The Boltons control Moat Cailin and much of the North, so getting to the Wall through Bolton territory is much harder than getting Sansa to Winterfell with the Boltons' permission, and there's no guarantee that Stannis would still be at Castle Black by the time they arrived
• Stannis may be less likely to work with someone with Littlefinger's reputation
• If Stannis loses, Littlefinger loses his foothold on the North

Why tell Cersei?

• It preempts her discovering Sansa's whereabouts for herself
• He ensures that Cersei won't try to intervene in the North, because he's said that he'll commit the Vale's forces instead
• It cuts off the Boltons from King's Landing, making their situation in the North slightly more precarious