Two tricks. In cooler to cold weather, double bags on your feet. First goes against your skin. Your usual socks, then a second bag, then I pull the thinnest stretchy sock I can find over that. Socks stay dry and insulating. You will want to wash your now soaking feet at the end of the day and rinse the insides of that pair of bags.
And cycling gaitors. I make them from windblock, slightly stretchy outdoor fabric. I make them as a wrap around my ankle. Top half is ankle circumference plus the width of velcro take. Bottom half is slightly bell shaped and about an inch bigger than the ankle section. Similar velcro. Tights or legwarmers go on over the gaitors.
I made mine for cycling boots. Work really well there. Then I discovered they also made my shoes far warmer in the rain but I wish I'd thought of that before I cut the fabric and I'd tailored them better for shoes. Even with the poor fit, my feet stay a lot drier and much warmer.