When babies and toddlers are learning to walk it's best for them to learn to walk without shoes.
When babies and toddlers are first learning to walk most of them are flat footed because of the bones and muscles as well as ligaments in the feet are underdeveloped and when the toddler walks barefoot it helps to encourage balance, posture and coordination.
Barefoot is best for toddlers to allow their feet to grow and develop.
When at home and in the house it's good for toddlers to go barefoot or at least wear just a pair of socks.
Shoes can be restricting and when possible the toddler should go without shoes.
Of course if the toddler is outside away from home they should wear shoes but at home they are best off barefoot.
If the toddlers feet are cold or the room is cool you should put socks on the toddler at night.
However if it's warm the toddler may be more comfortable sleeping without socks.
During winter months it's best to put socks on the toddler to keep their feet warm as they lose some body heat through their feet.