Is it possible to walk on a broken foot?

Yes it is. Directly after the trauma, when the patient is in shock and an endorphin reaction has set in, it may not even be very painful. Even afterwards, the pain may (or may not) be slight. This means that you can't always use extreme pain in order to diagnose a fracture. Also, this doesn't mean you SHOULD walk on a broken foot. If you suspect the foot is broken, the only way to rule that out is with an xray or similar scan. Always a good idea to get these checked.but before you get an xray you need to make sure the swelling goes down

Depends on which part of the foot you break.

The foot is generally quite stable, with several bones running parallel to each other and supporting each other. Me, I could walk - well, hobble - a minute or two but it hurt bad for several weeks.