Stannis Baratheon doesn't back down from a challenge. He probably doesnt even know how to, the sheer thought of it as shocking to him as killing your daughter would be to, well, almost anybody else. Despite the snow and the fact his forces may not make it to Winterfell, he continues to march forwards. When Ramsay leads a stealthy attack on his camp, destroying his food supply and a few of his men and horses, he doubles-down on his desire to go ahead with the attack. When his plans for a siege falter, as the Bolton army rides to meet his own, and his men are massively outnumbered, he simply draws his sword. When he believes so strongly in the cause hes fighting for, he will and does continue fighting until the very end, killing Bolton soldiers and doing what he can to survive even when the war is long since lost.