My feet freeze during the winter. I have taken to wearing the fuzzy socks under my dress boots. No one sees them and they keep my feet toasty warm. Outside of that, one could also keep a small fleece blanket with them (if in office or teaching). You can place it over your feet, under your desk, and no one sees!
As an avid hiker, I have always paid attention to the health of my feet. It is important to keep your feet dry during all seasons of the year, and in the winter doing so can help with cold feet. Using two layers of socks, thick over thin, can be very helpful, especially if the inner pair is make of a wicking material that does not absorb moisture, like polypropylene. You can also buy socks that are made with two layers already integrated; check out a hiking or sporting goods store. There are several manufacturers who produce specialty socks that are designed to keep feet both dry and warm. They are not inexpensive, but the comfort is worth it. If your feet seem to sweat a lot, using an antiperspirant spray on the soles and in the toe area daily will also help.
Good circulation is important. Make sure your socks and shoes are loose enough to allow for good blood flow. Also avoid clothing that binds around the lower parts of the body; for instance, knee highs or socks with an elastic top can be a problem, blocking blood flow. Try to move around and get the blood flowing on a regular basis, which is good for your whole body.
A very old fashioned cure for cold feet is to shake some ground red pepper into your socks before you put them on. Silly as it sounds, it works well. However the pepper will stain your socks and feet orange, so be forewarned if you try this.
I place a small heater so that it will blow on my feet. Cold feet are a constant problem of mine in the winter, even when other parts of my body feel perfectly warm. I'm sure there's some strange reason for that, but I am content not to know. Good luck. I have also heard of battery-warmed socks, but I haven't tried those.
Here in Florida, one pair of thick socks ususally do the trick. I wear bedroom slippers at night, but I miss the antique heated footstool I used to own. Of course, I wear no socks at all when I take my daily laps in the pool.
I find that wearing two pair of socks helps, especially if I am going to be outside for awhile. I really like to wear a moisture-wicking light sock and then a heavier sock over that. It is the sweaty/wet feet that get cold and then can't warm up. Those special socks really help keep feet dry and warm.
Well... short of moving to some place without winter, the best thing to do is to wear socks and slippers. I don't think there's any other way that's going to work well. Of course, the more you exercise and such, the warmer you'll be, but that wears off after a while. So I think that bundling up is the only way.