I presume all the items are packed in 仕覆（しふき）to convey a sense of warmth.

• Pick up 茶碗 in its 仕覆 like a 天目.
• I think it would be really nice to hang the 仕覆 on a tree or something if you really did the 点前 outside.

• For 懐石, the vibe is elegant 道具, humble food; so maybe the same applies here?
• Since you turn the lid, boxes with paintings are difficult; maybe some clouds pattern? I also like the style where the box is plain wood, and the corners are shaved off and lacquered.
• The books use a black lacquered box, and a light blue 仕覆 which seems suitable
• I'm doing this 点前 in January, so maybe bright red 茶器 might be suitable, like the 丸棗 or the 曙?　Maybe in a net basket instead of a 仕覆?
• Generally, 干し柿 I would find nice, maybe on a 筒茶碗?
• I got a 仕覆 with ducks on it, which I like a lot
• I really hate that hole for the 茶筅 in the inset, and I've seen 茶箱 that just do away with the entire corner to make room for it.
• A plum wood 茶杓 would be lovely, or with plum 蒔絵. Then the 仕覆 might be something with plum flowers.
• For the 茶巾筒, maybe some red-white painting with bamboo or pine covered in snow?
• 振出し could even be glass, go give an icicle feeling ⸺ but I also want to give them warmth, so maybe 備前 is better suited.
• And for the 古帛紗, maybe just find a nice 雪月花, 唐松 or just the trirune (maybe 和久田)? There is also a cute 雪兎 one, if I want to be more playful.