Wet and cold is the worst combo. There’s really not any good solutions.
One thing you can try for your feet is something like vapor barrier liners (VBLs), except put them on over an insulating layer, instead of close-to-feet with insulating layers on top like the usual application.
Wear a mid weight wool sock, and put plastic bags over the top (I use the ones you get at the grocery store for putting veggies and fruit in - light, and waterproof). Then put on your usual shoe covers.
If you do this, it’s important not to sweat, as if you do, your insulating later will get soaked with sweat.
If this is your first time riding with VBLs, it may be hit and miss experience. Bring a spare pair of socks in case you overheat and soak your initial pair.
Here’s a good overview of VBLs. The conditions you describe are not ideal for using VBLs, but can work to keep your feet dry (and warm) in the right conditions.