Okay, I'm gonna weigh in.
I tend to favor fatal endings for the damsels, but in this case I'm leaning toward a naughtier but survival-oriented plotline.
With a surge of strength and a little help from dear Godiva, the horse does indeed escape. However the suction of the mud is too much and she cannot hold on to his tail, so she remains trapped and sinking. The exhausted horse wanders off, covered in mud, leaving the poor noblewoman to perish horribly.
The very villagers she heard and tried to not be seen by find the muddy horse. Still fresh from the spectacle back in the streets, they recognize the steed immediately; seeing the mud they realize she must have cut through the deadly bog, and they hurry over, for why would the horse be alone?
Dear Lady Godiva has sunken to her breasts and is still going down when they find her. She is overjoyed to see them and begs for help. Unfortunately these are NOT the nicest of her peasants; they agree to help her, but not for free, and we aren't talking gold.
She is quite horrified by what they are suggesting and refuses most adamantly. She is, after all, a noblewoman.
As she sinks to her neck however fear for her life makes her change her mind. The men have her vow on her honor not to try to break the deal or have her husband punish them. Desperate, she does so, just before her mouth and nose go under.
They catch her flailing wrist with a lasso and pull her out before she suffocates.
At this point she either breaks her word of honor, snatching the watching horse's reins, or keeps her word...