Hot beverage cans from vending machines and heat packs from combini are useful for warming up your hands. Some heat packs are adhesive and meant to be pasted to clothing.

I also noticed stick on heat pack toe warmers adhered by a prepared traveler into her ryokan slippers. I'm not sure where she purchased them and would try Tokyu Hands, Loft, or DonKi? Some ryokans will also provide tabi socks. The non-slip kind is really useful if you visit more ryokans. I'd be tempted to layer a thin sock, adhesive toe warmer, and pop on some thicker socks for temples or castles which provide a plastic bag to carry your shoes.

If you can't tell, I get cold pretty easily so I like a few contingency plans