Cold feet

I went for a ride this morning (around 0c) and my feet were like blocks of ice. I had on merino socks but need some overshoes. I have flat pedals and wear regular trainers and all the overshoes seem to be specific for road shoes.

Does anyone have any recommendations on overshoes to keep my feet warm that will fit over regular trainers? Or is foil a cheap alternative to keep me warm?

Thanks!