If Ramsay did win a battle against stannis...

[Fightbringer]

why cant he find theon or arya, and why does he think they've gone north to castle black?

This question is probably true for two outcomes whether stannis has indeed been defeated and killed or if as many think, he has faked his own death in order to find a way to sneak he and his men into winterfell, but probably more relevant in the second, as in the first there would be the answer that stannis had lost so in desperation theon grabbed (f) arya, or was told to by someone, and rode north for the wall.

If Stannis does indeed have some kind of plan though, why would he send theon north (or at least away) with so important a person as who he perceives to be Arya, especially when judging by the gift chapter from tWoW he's planning on killing him, and his northern bannermen wouldn't accept anything less.

As I was writing this a couple of possible answers came to me for this

a) Stannis only sent (f) Arya up north, and theon escaped, ramsay assumes because jeyne has gone north, so has theon.

b) Stannis sent Theon to the wall so that Jon may execute himself, as it was his brothers he murdered , or because theon requested to take the black (unlikely stannis would grant the second one, and the first one would seem uncharacteristic of stannis since he believes in justice, not vengeance)

c) Theon has been revealed to be innocent of killing Bran and Rickon, so Stannis felt free to do what he want with him

What do people think?

[Gurkhal]

why cant he find theon or arya, and why does he think they've gone north to castle black?

This question is probably true for two outcomes whether stannis has indeed been defeated and killed or if as many think, he has faked his own death in order to find a way to sneak he and his men into winterfell, but probably more relevant in the second, as in the first there would be the answer that stannis had lost so in desperation theon grabbed (f) arya, or was told to by someone, and rode north for the wall.

If Stannis does indeed have some kind of plan though, why would he send theon north (or at least away) with so important a person as who he perceives to be Arya, especially when judging by the gift chapter from tWoW he's planning on killing him, and his northern bannermen wouldn't accept anything less.

As I was writing this a couple of possible answers came to me for this

a) Stannis only sent (f) Arya up north, and theon escaped, ramsay assumes because jeyne has gone north, so has theon.

B) Stannis sent Theon to the wall so that Jon may execute himself, as it was his brothers he murdered , or because theon requested to take the black (unlikely stannis would grant the second one, and the first one would seem uncharacteristic of stannis since he believes in justice, not vengeance)

c) Theon has been revealed to be innocent of killing Bran and Rickon, so Stannis felt free to do what he want with him

What do people think?

Stannis don't strike me as a trickster guy, so him faking his death to sneak into Winterfell feels overtly complicated and building a castle on water.

One reason as to why Ramsay hasn't captured Theon, Asha and Jeyne could also be that they have, if Ramsay did indeed defeat Stannis, escaped during the battle. Although this is a far stretch.

[RumHam]

By the end of the Theon Sample chapter Stannis has made it clear he intends to send "Arya" to Castle Black and execute Theon, one way or the other.

[Jon of the Dead]

Stannis has indeed sent Jeyne to the Wall already, but he didn't send Theon

I think it's very possible that Asha and her crew could plan an ambush to release Theon. As we know, Asha told Stannis to

behead Theon in front of the heart tree in the island of the frozen lake

It seems to me that it is an ideal place for an ambush, considering that Stannis won't take his whole army across the lake and that the blizzard provides the appropiate condition for hiding. Plus, it's a hell of an specific location, so Asha definetely has something planned, considering that if Theon dies so does her hope to beat Euron.

But if Ramsey didn't beat Stannis and what is in the pink letter is just Ramsey's assumptions, then he has no reason to think Stannis has Theon and Jeyne. As far as Ramsey knows (likely from torturing the spearwives) Mance was working under Jon/Mel's orders to bring Jeyne to the Wall.

[EstEst]

why cant he find theon or arya, and why does he think they've gone north to castle black?

As we know from the sample chapter,

Maester Tybald sent to Roose the map, could as well scribble couple of words in explanation. Including that Reek and fArya arrived in the camp accompanied with a bunch of Blacks (and the Banker that he doesn't know). That they're going to be sent to the Wall can be Ramsey's guess.