Osechi - an assortment of small dishes eaten on New Year's; Ozoni - a special soup with mochi eaten on New Year's; Fukuwarai - a traditional game, like "pin the tail on the donkey" but with a face instead; Sugoroku - a traditional board game
 Kanata makes two water puns with the previous line's mizuirazu ("private") and this line's mizukusai ("reserved"). Both have the kanji 水 "mizu", which means water.
Winter Sleeping Beauty - 2
 The original phrase used in pinky promises in Japanese is more like "If I lie, I'll drink a thousand needles". A thousand needles is pronounced harisenbon, which is also how you say porcupinefish/blowfish in Japanese. So the pun is harder to pick up in Japanese, but Kaoru kindly pointed it out for us.
Winter Sleeping Beauty - 3
 Every dish in osechi has a special meaning. In order of appearance:
1) Kuromame (black beans) are a pun on mamemameshii ("hard-working, diligent").
2) Shrimp carries a meaning of longevity and is a must-have in osechi, so while the CG shows Kanata eating a lobster, he might be calling it a shrimpy on purpose.
3) Mackerel carries the meaning of fortune, and eating it will bring an auspicious year.