Very good question!
Short answer – very well, if prepared!
Winter Barefoot Walking is not for the unprepared!
The main thing is to keep the rest of your body toasty warm by wearing thick insulated warm clothing & a hat.
It is also important to keep your legs and ankles warm, perhaps with leggings etc.
The foot needs time & gradual stimulation over months to adapt & acclimatise to the cold.
Firstly, after walking and running barefoot for a few months during warmer weather, the soles of the foot develop thick, flexible, insulating & protective layers of skin which keep out most of the cold from ground contact.
Another adaption for the cold is that blood flow is increased by unrestricted foot movement & therefore a stronger blood pumping action is achieved than is possible in constrictive footwear.
Also increased muscle activity (due to the foot muscles needing to work harder without the support of footwear) generates heat within the foot itself thus keeping it warm.
The next two points are conjecture as to how our bodies adapt to cope with cold.
Some people think the blood supply increases just due to cold exposure in order to keep the feet warm to protect them from the potential freezing effect of the cold. Of course this wouldn’t happen if the core body temperature drops which would then drain the peripheries of blood to protect the vital organs to the detriment of the feet & hands. So it’s vital to keep the rest of the body toasty warm.
Another possible adaption is that the nerve endings which would normally react painfully to the cold, do adapt by moderating the sensation so that you don’t feel intense pain. This could work in the same way as nerve endings adapt to the initially painful sensation of touch on rough surfaces. It is possible that the only reason we feel intense pain from cold is that we are not used to feeling that particular sensation, so the nerve endings are at first ‘dazzled’ by the over-abundance of sensory nerve sensation, but moderate with continued gradual increase in exposure till the sensation normalises.
It is possible to cope with temperatures below freezing as long as you are careful.
It is especially important to “keep moving!” Otherwise the increase in blood flow & increase in muscle-generated heat will not occur.
I only have limited experience, of one winter, but apart from just a couple of times where I wore sandals for insulation & once my FiveFingers, I managed most of the winter comfortably barefoot.
I did regularly hike through the winter for upto an hour & half even on snow & ice at around freezing point or just below with only one experience of mild freeze injury to the skin, which resulted in slight skin sloughing later. Though it was my first winter last year & I had only been totally barefoot for six months.
Now my skin is tougher I’m expecting even better results.
The other important point is that everyone is different & respond differently to cold so may be it’s not possible for everyone to go barefoot in winter.
Some people have circulatory disorders, including Raynauds disease for example, which could preclude them from ever attempting barefoot walking in winter.
Being sensible is the key to avoiding serious injuries.