Cold feet at nursery

My LO has just started nursery. She can’t walk yet, but can stand unaided. She doesn’t wear shoes, only socks. I’ve noticed that when I pick her up, her feet are absolutely frozen. They are soooo cold and even when I’ve got her home it takes quite a while to come back to a normal temp. Any suggestions on what to do about this? She’s big for her age so she can’t fit in soft booties. I can’t put fluffy socks on top as she needs the grips whilst she’s standing and trying to take a step