Personally, I hate wearing socks. Only wear them if I absolutely have too. I also hate searching for the missing dck's sock at the end of the day, as they notoriously take them off and hide them in toy cupboards, kitchens etc...so...I prefer they actually not have socks on in the house.
Outside they wear socks and running shoes (unless a parent has sent them in sandals). Those in sandals have their feet wiped down with a baby wipe when they come in the door so that they don't transfer too much dirt onto my floors. Those who worse socks and shoes take them BOTH off at the door and then go up to the daycare rooms.
If I ever noticed something like warts etc that could be transferred to the other children or my family I would insist they have socks on at all times though...