Except, Manderly won't fight Stannis at all. I'm not quite certain of his sympathies, but we know at least of his enmities: the Freys (over the Red Wedding) and the Bastard of Bolton (in the dispute over Lady Hornwood's treatment, and her land.) While he turned to support Roose because of the lack of any credible alternative power in the North, now there *is* a credible alternative power (Stannis)... and Manderly believes that Stannis now has a free Arya Stark who could be put up as *a* Stark in Winterfell. Stannis knows of Arnolf Karstark's treachery, and has him under arrest. The Freys are doomed, everybody hates them now, with the Boltons (and the now-fragile Lannisters in the south, who have lost Tywin, Kevan *and* Tyrion) being the only people who don't actively want them dead, and even the Boltons and Lannisters probably despise the Freys as tools even while they use them. Manderly, outside of Roose's control, may turn on them even before either side meets Stannis.
Of course, Ramsay the Bastard, who isn't stupid, probably guesses all this about Manderly and the Freys. (So, in all probability, does Roose.) If so, the plan may be for Ramsay's host and the Freys to expect Manderly to change sides already, and be ready to turn on them, which may in turn force Stannis to come to Manderly's rescue and commit to battle earlier than he would have liked, and possibly not in the position he hoped. In which, of course, the treachery of Arnolf Karstark would play a crucial part in defeating and scattering Stannis's host... But, importantly, the Boltons do NOT know that Arnolf Karstark is under arrest, so when the Karstark men will turn up on the field obeying the orders of their new commanders (as soldiers do), it will be under Stannis's leadership, and it's the Bolton army that will be routed.
As for the letter... The fact that Ramsay signs it "The True Lord of Winterfell" means that it must be a tactical lie: any letter sent north should have been signed by his father (Ramsay himself cannot be a lord while his father lives, nor should be sending any communications without his father's name attached unless there is some deception intended.) I guess the Boltons are either expecting a crashing defeat or have just had one.
Edited by JLE, 15 March 2013 - 05:07 PM.