As there have not been (as of A Dance With Dragons) any Roose PoV chapters or any chapter where he talked about this battle, we may only speculate on his reasoning.
This article speculates, with varying amounts of evidence that Bolton, while not exactly an ally to the Lannisters since the beginning, was certainly disloyal to the Starks, trying to further his own ambitions while undermining the strength of his liege lord and his loyal bannermen.
Regarding this specific battle, we can see two interesting quotes from the book that show that Bolton's forces haven't suffered so much in this defeat:
He glimpsed the bull moose of the Hornwoods, the Karstark sunburst, Lord Cerwyn’s battle-axe, and the mailed fist of the Glovers ... and the twin towers of Frey. (AGOT, Tyrion VIII)
“My liege, we have taken some of their commanders. Lord Cerwyn, Ser Wylis Manderly, Harrion Karstark, four Freys. Lord Hornwood is dead, and I fear Roose Bolton has escaped us.” (AGOT, Tyrion VIII)
This has not been the last time Roose Bolton's forces had separated from the remaining bannermen's, to their loss. At the Battle of Duskendale, which was Roose Bolton's idea (to which he did not commit any forces), he had similarly sacrificed the lives of his "allies" as opposed to his own:
“Tell him to put the captives to the sword and the castle to the torch, by command of the king. Then he is to join forces with Robett Glover and strike east toward Duskendale. Those are rich lands, and hardly touched by the fighting. It is time they had a taste. Glover has lost a castle, and Tallhart a son. Let them take their vengeance on Duskendale.” (ACOK, Arya X)
"As for Stark, the boy is still in the west, but a large force of northmen under Helman Tallhart and Robett Glover are descending toward Duskendale. I’ve sent Lord Tarly to meet them, while Ser Gregor drives up the kingsroad to cut off their retreat. Tallhart and Glover will be caught between them, with a third of Stark’s strength.”
“Duskendale?” There was nothing at Duskendale worth such a risk. Had the Young Wolf finally blundered? (ASOS, Tyrion I)
The result was a large defeat for the North:
The eunuch smiled a silken smile. “I have such delicious tidings for you all, my lords. Yesterday at dawn our brave Lord Randyll caught Robett Glover outside Duskendale and trapped him against the sea. Losses were heavy on both sides, but in the end our loyal men prevailed. Ser Helman Tallhart is reported dead, with a thousand others. Robett Glover leads the survivors back toward Harrenhal in bloody disarray, little dreaming he will find valiant Ser Gregor and his stalwarts athwart his path.” (ASOS, Tyrion III)
When they brought him word of the battle at Duskendale, where Lord Randyll Tarly had shattered Robett Glover and Ser Helman Tallhart, he might have been expected to rage. Instead he’d stared in dumb disbelief and said, “Duskendale, on the narrow sea? Why would they go to Duskendale?” He’d shook his head, bewildered. “A third of my foot, lost for Duskendale?” (ASOS, Catelyn IV)
Not only that, when Roose Bolton left Harrenhall to rejoin the Starks, more loyal bannermen fell:
Two-thirds of my strength was on the north side when the Lannisters attacked those still waiting to cross. Norrey, Locke, and Burley men chiefly, with Ser Wylis Manderly and his White Harbor knights as rear guard. I was on the wrong side of the Trident, powerless to help them. Ser Wylis rallied our men as best he could, but Gregor Clegane attacked with heavy horse and drove them into the river. As many drowned as were cut down. More fled, and the rest were taken captive.” (ASOS, Catelyn VI)
Roose Bolton's caution has been proven in all of these interactions. What is to be questioned is his loyalty. Which the event of the Red Wedding has proven.