What is that it says about "...is dead from wounds he took in a..."?
Arya has been on her own since the end of Season 1 basically, she's only just made it back to her family, and a few days after she gets back, she see's the Lords of the North pretty much straight up plotting against Jon, what would you think?
Arya and Sansa were never on the best terms anyway.
We don't know what's Arya going to do with it. I mean, she saw Littlefinger plotting and she knows what he's capable of, so she might do some more investigating and outsmart him - which the spoilers (the ones that have been 100% correct so far) are kinda pointing towards, seeing as how Littlefinger is to be sentenced to death by Sansa and killed by Arya at the end of the season.
Naw, I think all this is leading to Arya finally getting to shank Littlefinger.
She's suspicious of Sansa, but I highly doubt she's gonna kill her before she confronts her about it, Sansa will tell her what the letter was about, then Sansa will finally realise that Littlefinger is never gonna be on anyones side but his own.
I wouldn't be surprised if it came out that Littlefinger was the one pushing the Northern/Vale Lords into questioning Jons leadership.
Because it was him.
Littlefinger's plan is simple - he wants Sansa to be declared Queen, so that he can manipulate her into marrying him, thus making Littlefinger the King in the North. In order for this to work, he needs to make the northern lords lose faith in Jon - which he's doing.
Also, on the topic of northern lords...
Lord Glover is such a cunt! He first refused to help Jon (which I kinda do understand, because it might have looked like a lost cause to him), but was a bitch about it, then "a man can only admit to when he was wrong" happened and he has sworn loyalty to Jon, only to speak out against him and support another candidate to the throne.