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My set up for the last few years has been mudguards, neoprene overshoes and/or waterproof socks. If my shoes are wet when I arrive at work, I stuff them with newspaper and put them next to a radiator. Socks get changed to some non waterproof ones, waterproof socks and overshoes also go next to the radiator. Nice dry, toasty feet for the ride home.
Having said that, I would really like some proper winter shoes.
I’m using neoprene at the moment but feet and shoes are getting wet. They’re not drying much over the day and putting wet shoes back on is grim - and they’re getting smelly because they’re wet for so long.