Have you tried trousers?
I always put up with cold wet feet until I did some winter bivvy rides and thought I should take a bit more care over staying warm and dry.
I bought some MT500 spray trousers and wore my salomon goretex hiking boots. I’ve got a few pairs of flat pedals, they didn’t work well at all on the set that was on the bike, but were absolutely fine on the Superstars. I left the bottom few inches of the cuff unzipped so they’d go over the tops of the boots. Lovely.
I’ve ridden in the trousers a fair bit since with normal flats (5.10 freerider pro, Ions) with the same arrangement with leaving a bit of flare in the trouser cuffs to cover the bit where your foot goes in. Mostly dry and toasty! Keeping legs and socks dry and the top of the laces covered is 80% of the job, I reckon.