I've been using
Sugoi shoe covers for many years.
They are waterproof and warm, with a fleece inside, and they fit snugly. Plus, the Sugoi site has the on sale.
Water still gets in through the bottom, so I've put duct tape over the shoe soles' bottom vents.
Even so, a little water gets in eventually. I hang up my shoes inside the water heater closet to dry them out overnight. Taking out the insole helps.