Is it permissible for someone whose foot is in a cast to perform ablution by wiping over their toes without wiping over the cast itself?

The fingers must be washed, not just wiped. The splint that covers what must be washed during ablution (wudu') must be wiped. Not wiping the splint invalidates ablution according to the majority of scholars. Since the questioner neglected washing his fingers and wiping the splint, his ablution is invalid, and he must repeat the prayers he performed with that ablution.