Will Roose send Ramsay to attack Stannis?

Now we know from Theon I DwD that Freys and Manderlys are being sent to attack Stannis. In Asha I we saw that Hosteen and his men arrived, but in Theon I WoW hensaid Ramsay will be there, too.
In text Jeyne will be called Arya because as far as Roose and other Northmen are concerned girl is Arya.
At first I dissmissed this as Theon talking anything to save his life. But then I thought a little and came to idea that seems like somehing Roose would do.
He is well aware of his position in WF and Ramsays reputation amd his relations with other Northmem (Dustins and Ryswells are most important).
He told Theon a lot of important things in Reek III, but he told them for reason. First thing he said is that he knows Theons task. Then he sais he controls Ramsays men (who are also in huge trouble now because Sour Alyn and Grunt are dead people walking) which plants seed of suspicion in Ramsays head. Then he sais something weird: he knows Ramsay killed Domeric and will allow him to kill any son he has with Walda. This prevents Ramsay from thinking to kill Roose and makes Ramsay feel safe, just like Robb felt safe... and Tywin before (although that didnt go so well, but you see my point).
So what does Roose plan to do with Ramsay? My guess is wait for Arya to have a son and then kil Ramsay. Ramsay cant be lord of WF, too unreliable, and Roose is smart enough to see that it means destruction of house Bolton.
But now Arya is gone and Ramsay is no longer needed.
If Ramsay somehow dies in battle (which is not unlikely amd Roosemis probably well aware of it) he can make his heirs (I think he planned to raise an worthy heir anyway, he is not that old after all) and have better situation among Northmen (most importantly Dustins and Ryswells) and he will have less mouth to feed (we saw in Theons chapters that they would have had a food problem, not serious lkke Stannis, but a problem anyway) amd WF can be defended with 3k men against 4 or 5k freezing men (maybe less).
If Ramsay wins he can kill him differently, but it would have been suspicious, this was perfect because we have Stannis on one side and Hosteen and Ramsay on other and there is a proverb: An army of donkeys led by lion beats army of lions led by donkey.
But what about Arya? Well if she dies, shs dies. But if she lives there are two options:
1) Ramsay and Freys are defeated so Walda lost her purpose and Arya has a purpose (kill Walda and marry Arya himself).
2) Ramsay wins so he can pull RW 2.0 and kill Freys while they were feasting after victory. This would please Northmen (they might even take a part in revenge). He can also sally out to attack them to avoid breaking of guest rights, but it doesnt matter since this scenario wont happen. Still has Arya for himself. So he can chose between Ramsay hurting Arya and him marring her and treating her like she deserves (which he would clearly do), one pisses off Northmen, other makes them tolerate them, but this scenario is least likely of all 4 and I guess Roose doesnt count this to happen at all because this is worst case scenario (bunch of Freys live, Ramsay lives and Arya is back).
If Arya dies or escapes for good there are two more scenarios:
1) Ramsay dies and he marries woman from North, maybe Lady Barbrey.
2) Ramsay wins and he stays married to Walda because only Ara is worth betraying Freys.
But I think that Roose thinks it is most likely for Ramsay to die (not enough men facing superior commander with motivated army and his army is deeply divided) and him to search for another bride Arya or Barbrey most likely.
To sum what I said: Ramsay can do much more damage than he can help and he can gain much more by sending him to find his bride and kill Stannis but in fact he is sending him to his death so he can restore peace in North. If Ramsay stays in WF he can only cause problems, big ones. So he has to die, but the best way is to die in battle because it makes Roose not being suspect (after all Roose did say Bolton men are his, they all can turn on him, like Gold Cloaks on Ned).
Also it is worth mentioning that Roose can find some Mandon Moore with order to kill Ramsay in battle.
Maybe a bit too confusing, feel free to ask me if you don't get some part.
What do you think, will Roose send Ramsay to attack Stannis and what are his plans?
I am looking forward to hear your opinion.