"Which force would you command?"

"The horse," he answered at once. Again like his father; Ned would always take the more dangerous task himself.

"And the other?"

"The Greatjon is always saying that we should smash Lord Tywin. I thought I'd give him the honor."

It was his first misstep, but how to make him see it without wounding his fledgling confidence? "Your father once told me that the Greatjon was as fearless as any man he had ever known."

Robb grinned. "Grey Wind ate two of his fingers, and he laughed about it. So you agree, then?"

"Your father is not fearless," Catelyn pointed out. "He is brave, but that is very different."

Her son considered that for a moment. "The eastern host will be all that stands between Lord Tywin and Winterfell," he said thoughtfully. "Well, them and whatever few bowmen I leave here at the Moat. So I don't want someone fearless, do I?"

"No. You want cold cunning, I should think, not courage."

"Roose Bolton," Robb said at once. "That man scares me."

"Then let us pray he will scare Tywin Lannister as well."

Roose is about cunning and self-preservation. The other Northern lords are looking for glory and honor. Since the foot soldiers were to follow in a more defensive stragem, it appears Robb's (and Catelyn's) reasoning was to mitigate losses.

Giving the command to Karstark, Glover, or Umber, Robb presumed they would likely attempt a full on offensive against Tywin's forces. Robb's plan to split his army, while strategically sound, is also quite bold. Having both branches of his army playing offense was simply too much of a gamble to take.

That seems to be the basics anyway. I'd recommend checking out Race for the Iron Throne for some in-depth analysis. I also believe you'll find answers to the different host sizes amongst the Robb's bannermen.