Needing opinions !!

[Lee-Bee]

Sounds like it's many little things and not just the sock issue.

But, at 4yrs old she is old enough to negotiate and accept a compromise. If the child was already used to you being in charge and accepting your authority I would suggest sitting down and discussing a compromise. She can go barefoot inside on the condition she puts her socks on with no complaint to go outside each day and that the first time she complains about cold feet she has to put her socks on the for the rest of the day, with no complaints. This would give her ownership of the socks while not negatively affecting your day.

BUT, it sounds like she might not be able to put the socks on without complaint when she needs to go outside. This is a whole other issue and would likely make it much harder on you.