It is common for people to wear thick socks, hats, mittens, and jackets, but wear next to nothing on their legs. I guess we just don't feel the cold as much on our legs as in other places, but you lose heat from your legs just the same.
So, to warm your feet, be sure to insulate your legs. I wear thermal undies and knee-length thick wool socks (note...I found these way too warm when I was young so I put them into long-term storage...now they are just the thing!). Friends have worn thermal "leggings" that insulate from ankle to a little below the knee.
And don't forget to wear something on your legs to cut the wind if the wind picks up.
Finally, three more things: down booties, down booties, down booties!