In Season 5 Episode 10 (Mother's Mercy) of Game of Thrones, we see the Boltons attack Stannis' army. It seems that the Bolton's army is FAR larger than Stannis'. Is this true? Do we know how many soldiers Stannis and the Boltons had at this time?
As of season 2 there are 20,000 northmen in the Riverlands.
After all the fighting, backstabbing (e.g. Red Wedding), blackmails etc. it is guesswork. Also most of the men Roose has aren’t actually loyal per se.
From the book:
Winterfell is held by Lord Roose Bolton and his legitimized bastard son, Ramsay. His force, aside from the strength of House Bolton, consists of a few thousand of Houses Frey, Ryswell, Dustin, Cerwyn, Hornwood, Manderly, and the other half of House Umber under Hother "Whoresbane" Umber.
Although Roose has the larger host, and his soldiers are far better armed and trained than the clansmen that make up a large part of Stannis's army, the loyalties of some of his forces are highly questionable, particularly the Manderlys, Whoresbane Umber, and the Hornwoods. Roose suspects that only the Freys, Dustins, and his own men would be truly loyal to him if word gets out that Bran and Rickon Stark are still alive.
Winterfell is overcrowded with forces, low on supplies, and on edge due to a series of murders with no confirmed suspects.
Cut that in half as not all of the North declared for Roose, and you are down to 10,000.
Out of those we know that:
After the murder of Little Walder Frey and the near battle inside Winterfell between the Freys and Manderlys, Roose Bolton, fearing another battle inside the castle between his own forces, sends out Hosteen Frey and Aenys Frey along with the 2,000 Freys to engage Stannis's host.
The Freys' presence increases tensions with the northerners as many had lost kin at the Red Wedding. Roose also sends out the forces of Lord Wyman Manderly as he does not trust the Manderly forces. Ramsay Bolton follows not far behind, with a force of his own Dreadfort men. The absence of near 3,000 men in Winterfell also means that Roose also has an easier time managing food supplies to his forces.
So 10,000 - 3000 = 7000 men. Of those maybe 2-3000 are Bolton men.
This is part speculation, part facts from the book. So this differs greatly from the show where Stannis is defeated in front of Winterfell.