Bare feet in public in winter

How do you keep a baby’s feet warm in winter when they take off nearly every shoe and sock by the time you reach your destination? Especially for babies in convertible car seats where you can’t just keep a blanket on them and bring the infant seat in the stroller system, but you have to take them out and they’re only covered by what they’re wearing?

It’s getting colder, and weeks of trying to get my 10 month old to keep stuff on her feet isn’t working. I’ve tried various kinds of shoes, trying to teach her to keep stuff on, idk what else to try. I’m running out of time before this is truly an issue. Pretty soon we’re going to have to switch to her convertible seat and blankets, which are the only option that works so far, are not going to be an option for when I have to bring her into the store. Do I just blanket her in the car, and then reput her shoes on when we get there? That takes like 5 minutes and I feel like having the door open blasting her with cold air is worse than the 30 seconds it would take to carry her into a warm building and THEN put her shoes and socks BACK ON, but I get the sense that people will think I’m abusive or neglectful that way. But seriously idk what to do anymore she takes EVERYTHING off. I’ve considered zip up one piece suits but the problem with that is she’s long and they don’t seem to come long enough, and putting it over her clothes would 1) be too bulky to get a safe fit for the car seat and 2) be WAY too warm over her clothes once we get inside where we’re going. HELP