outdoor attire and clothing for feet and with carrier

I'm having trouble figuring out how to make sure our 2 month old is dressed warm enough in the carrier? What do you put on there feet? My LOs feet had socks, onesie, and thick outdoor snowsuit thing and still his feet were frozen after 1 hr. Was pretty upset by it. Or should we just not use the carrier when colder out? He likes to be held a lot and we can use the stroller at certain times of the day but mostly the carrier works better.