My LO is 7 mths too and I don't let him wear socks at all at home but only when we go out for a family outing. Their body is still regulating their body temperature so it's normal for them to feel cold on their feet but you can feel her true body temperature on her stomach or armpit. We are living in a humid country. Even the whites in a 4 season country let their LO explore their toes w/o wearing socks/shoes until they're bigger or in the cold season. By now your LO should be putting her toes into her mouth already, to explore.
I only let my LO wear socks during night sleep time because usually I don't cover her with blanket. She is going 1 year old and has been wearing since birth. I think don't wear during the day and just wear at night when she sleeps