I’d wear knee socks at this time of year, so no cold gap. Uniqlo do some fine ones in different colours, including a burgundy HeatGen thermal one which would match your shoes.
I find the key is either to match the sock colour to the shoes or to the trousers so as not to break up the line of your legs. Or make the trousers and the shoes the same colour and add a pop of something different with the socks.
Maybe it’s just me, but if I don’t do that, I end up feeling like a toddler.