Well, I got the mask present, and I put it on some cousins, and they got...odd:
- :shikao Shikao: His head turns into a real TV
- :macho Macho: His face tries to leave his body (lol!).
- :cancan Can Can: His face turns into a lamp.
- :nik Nik: A lion mask, nothing odd.
- :slip Slip: His face gets bigger.
- :lamour L'Amour: A heart mask.
- :jungle Jungle: A leaf mask.
- :huey Huey: His face turns into another antenna.
- :nickel Nickel: A boxing mask.
- :honey Honey: A bow on her face.
- :beyond Beyond: A toucan mask.
- :twinkle Twinkle: This is really funny: two more spires. It looks like a hedgehog.
- :fujio Fujio: A typical thief mask.
- :miso Miso: No face, just a bowl! xD
- :havana Havana: Red Ridding Havana.
- :prince The Prince: A known fox.
- :peso Peso: Another dot.
- :drooby Drooby: A demon mask.
- :dipp Dipp: A disco ball xD
- :johnson Johnson: All his head turns into an alligator.
- :june June: His face opens and a bird comes out, like a clock xD.
- :daisy Daisy: Guess it. A cow mask.
- :kuro Kuro: A robo-mask.
- :velvet Velvet: Same as June, but now The Prince comes out xDDD.
- :shy Shy: A cork shuts the little hole where his face is.
- :ace Ace: His head turns into a fish.
- :lalala Lalala: A head band.
- :kinoko Kinoko: All the head changes the pattern of the colours. This cousin is really funny, try to put any other head present on her (i'm not sure, maybe she's male!)
- :colombo Colombo: Birdy.
- :odeon Odeon: Lol, his face turns into a helmet.
- :nutsuo Nutsuo: His (again, not sure) upper part of the head/body turns into a monster.
- :opeo Opeo: Extra bandage on his head.
- :odeko Odeko: An Affrican mask, I think.
- :miki Miki: Blue Ridding Miki. It's very repetitive, 3 cousins wearing a hood...
- :signolo Signolo: A regular face in his three faces.

Tell me if I forgot any cousin.

PD: Don't mind the edition, I pressed Enter without meaning it.

is this real? i never knew about any of this!
how fun.

Yeah, I think this one is the funniest present you can wear xDD

EDIT: Use Miso :miso wearing the mask and with the buddy, I think this one is the best. It looks like the buddy is telling the way to Miso :miso xD

this happens in MMK and BK I believe too. Some of the other presents vary among cousins too. the moustache's change, colors of clothes, the guitars. I had started to make a faq for it but never finished it.

how awesome. thanks guys.
i always went for the giraffe head and nothing else really. didnt try to experiment with any masks.

Wow, thanks for the complete list! I was always too lazy to see what they looked like on everyone.