What reasons kept Godfrey from confessing to his father the next morning?What does this show about him?

Godfrey is slimy. He does a quick cost/benefit analysis about telling the truth. He figures telling his father only part of the truth will mitigate his (father's) anger and buy him some time to keep Molly and baby a secret. The death of the horse might give cause to his brother's disappearance which might distract father from his anger.