Goofy's line as he sang while bumping into a sign, causing icicles hanging from it to go flying into a small snow bump to make a 'fireplace'.
The funny sequence of what the Prince does to Donald during his lesson; Mickey naming the three secondary trigonometric ratios while using his pea shooter on Donald, before the duck tried to shoot a candle at the Prince, but he accidentally hit Horace's butt instead, causing him to yell out in a high-pitched voice.
Horace: Sire, we have been through this time and time again. It's hypotenuse. Hypote- (gets hit in the butt, high-pitched) -NUUUUUUSE!!
The Prince mocking Donald while mimicking Horace behind his back.
Donald:(points at the Prince) But he started it— Horace: Donald! (he and the Prince point to the door) (Donald leaves in a huff, grumbling)
Mickey slipping and bumping into a suit of armor, causing its helmet to fall onto his head while getting other suits of armor to fall apart in a domino effect.
A Weasel guard's reaction after hearing Pete booting out the actual Prince.
Weasel guard: (spits out beer in shock) You threw out the prince?! (laughs, doing 'shame, shame' hand gesture to him) You're gonna get it! You're gonna get it! NYAH-NYAH-NYAH-NYAH-NYAH, NYA— (Pete suddenly grabs the Weasel by the throat, making him stick his tongue out with a hilarious facial expression.)
Goofy trying to use a feather duster for a weapon, which wilted with a silly wilting sound.
A Weasel guard's wild take after the executioner- Goofy in disguise- slipped on a water bucket and accidentally threw the axe towards him, making the weasel scream in a wild take.
Right afterwards, when Goofy pulled the axe off the wall, the bladed end broke off and clanged the weasel on the head.
Goofy: (to the dazed Weasel guard) You wouldn't happen to have an axe I could borrow, would ya?
Weasel guard: (dazedly) Thank you. (gives Goofy a wet kiss on the nose) I've had a lovely evening. (faints to the ground with a crash)
Mickey trying to stall for time waiting for the real Prince at the coronation, with the owl archbishop thinking he's picked an inconvenient time to play jokes.
Archbishop: Now, Your Highness, if you will take your place...
Mickey: Uhh, after you!
Archbishop:(chuckles) Oh, beauty before age, Sire.