For rain-proof footwear I use the Adidas Five Ten Trailcross Goretex:
https://www.adidas.fr/chaussure-de-v...ex/S29146.html
I've not tried them in very cold weather (<5C), but I find them a bit too warm in mid-summer (>30C).
They work on any flat pedal. I have Acros:
https://acros-components.com/pedale/xl-pedal?c=88