It isn't clear from this post whether the CM stopped the car at the intended destination, or whether she was fed up of the child not complying with a request, so dramatically stopped, parked up, demonstrated and said, "Look, this is what the ground feels like - you need those shoes on."
A consequence that the adult models is not a ' natural' consequence, because it's an artificially engenderd result. Letting the child leave the car on arrival, spontaneously, and them experiencing the feeling of wet ground on their skin is a natural result.
Evidently, the context of this situation is significant because if the CM has three children to care for, for example, what do they do if one child refuses a request? When outdoors. If all the kids are going to the park, you could say, " You'll have to use the buggy, if you don't want shoes, as I am not allowed to leave you in the car, and the others want to use the swings."
If a child often didn't want to do particular activities which had been planned, I'd be thinking they ought to have their own dedicated carer, as I don't see that a CM can ethically-speaking force one child to come along outside to accommodate the wishes of the others. A dedicated caregiver might be optimum for a child experiencing behavioural challenges, since hitting or biting: if the other children are on the receiving end, it will become hard fro the CM to cope with the group.
Being in charge of a few children might be why she didn't take time to ask OPs DD what was wrong, because in her position, I would want to establish whether the DD removed her shoes and socks to indicate that she wasn't keen on this outing and the thought of going outside. Maybe she didn't want to go to the park and it's her saying of signalling this. Actually, what does the CM do then, with other children in her care and conflicting wishes? I guess it would depend on the personalities of the children in the group.
If the DD was very upset about the 'consequence' , I don't think it achieved the intended objective. Children don't learn meaningfully from being made to feel upset and even shocked. If the child had tried to exit the car barefoot, she might have extended one toe, found it was cold on the ground, and withdrawn it back into the warm. Nobody voluntarily places both feet down squarely on the tarmac, as would happen when placed there by an adult.
So, if a puppy poohs on the lino, are we to conjecture that the old-fashioned and derided expedient of pushing it's nose into its waste is a way of teaching a puppy a ' natural consequence' is that uncovered pooh in the wrong place might get stuck on the nose? Or is the owner doing this just creating an association between strong, smelly pooh and not having the pooh in the right place? Or is it a punishment ? How we explain that experiment is open to different interpretations ( as is the bare feet experiment) but clearly a dog playfully sniffing its own pooh would be a different experience for them than having their nose forced into it.