Hink-Pink

wail tail, cry lie, tearful earful

book crook

"Odder trouble" does not have a specific meaning. It could be interpreted as a more unusual or peculiar type of problem or difficulty.

cattle battle

fun run

Hush brush

Silly Filly.

richer pitcher

Assuming that you meant "What are the titles of the female horse?" Here are your answers:

Mare = A female horse over four years old.

Filly = A female horse under four years old.

"horse course" -- not quite a rhyme but maybe close enough.

Think about Christmas = Remember December

Playwright Harold's snow season = Pinter's winter

Radiant precipitation = snow glow

Frozen sin = ice vice

slight fight, small brawl, minute dispute

phony pony

smashing dashing, stunning running

Bony Pony or Spare Mare

cattle battle

fight knight

"Get wet" is a Hink Pink for "jump in the pool."

brighter fighter

silly filly

ghoul pool

Spring King

plump ump

pig jig
pig jig

beef thief