They do make/sell several items that may be useful. If I had to guess your desire would be to have "heating socks" that are fully mobile and are not an impediment to movement. I don't have much to offer there. For a relatively fixed situation I wonder about the following:
A. Heating pad (electric) such as you might apply to a sore back - more or less a small electric blanket. You might arrange that vertically or nearly so, where you sit, so that it is behind your legs. I mention this because these items are relatively safe and made for such an application.
B. They do make electric heating pads or mats that lay flat on the floor. While it does not address more than the sole of your foot this might provide some relief - and eases the burden of batteries for electric socks.
C. They do make electric or hot water radiant panel heaters. Usually a flat, relatively warm surface that is horizontal or vertical. These are usually made for fixed locations. The advantage of these - they are moderately warm rather than scorching hot.
If I had a similar problem I'd consider creating a smaller version of what we had in the house when I was a kid. We had a coal/wood furnace in the basement and one rather large metal grille in the floor where heat would rise. On cold mornings that's where we'd go to warm up.
Consider a box as a plenum with a perforated plate on top with an amount of warm air blowing upward. As with anything, you'd have to be sure you built in appropriate safety features.