There are many patents associated with foot warmer/lanterns for wagons and buggies. The early ones had a lantern below and in front of the wagon to light the dirt roads and vents to make the heat from the flame keep your feet warm. Doesn't seem like it would be too effective, but anything was worth a try I guess. Later ones were portable like yours and had a kerosene tank and burner to heat up the top of the foot rest, very little light was put out.
I will look through some patents to see if I can find anything like yours.
It would be easier to identify if you could find any markings like the manufacturer, patent dates, or patent numbers.
John M