You don't say what you have, only that you do not have proper footwear. Thus, my answer is sort of generic.

Most bike shoes have very good venting with mesh panels that work against your attempts to stay warm and dry. A plastic bag (shopping bag, bag from the produce aisle) over your socks but inside your shoes is not breathable so it is not a great remedy for all day, but works quite well for an hour or two. After a couple hours your feet will however get damp from sweat, so this is not a good all day solution.

I ran across a used pair of bike shoes a couple years ago for cheap, they were one size too large. I bought them for winter riding with my heavy wool socks. With the plastic bags over the socks they work great for a few hours down into the 20s.

For colder than 20s or longer than a few hours, I use lightweight hiking boots. For winter I switch to pedals that take cleats on one side, platform on the other. I use both Shimano A530 and M324 on differnet bikes. That allows me to use the hiking boots on the colder wetter days.

Are you out on a tour somewhere?