I have different shoes for different seasons - I'm wearing 5-10s now but they are too hot for a Balkan summer, so wore much lighter trail running shoes for TCR.
I recommend sealskinz socks. I had a pair on TCR last year and another pair of summer socks. I had issues with the latter and had to wear the Sealskinz. They were comfortable for a couple of days, even in 40 degree heat.
But warm hands and feet is more about keeping your core temperature up than loads of thick socks, so an extra base layer might be what you need.
I also don't mind riding in the cold and in the wet, but not both at the same time - other than commuting or short errands. Certainly not for pleasure, as it isn't