Seeing a 2 year old in a car park with no socks or coat on in this weather would certainly make me do a double take tbh.
True! Except the child wasn't 'in a car park' as such, they were in brief transit between warm pram and warm car, with blankets etc. and stopping the parent to have a chat about it would lead to this taking longer and the toddler getting cold, so that is of no use at all.
A couple of my kids tended to run very warm and were always pulling off their shoes and socks off even in low temperatures, so I would pick my moment to put them back on so they didn't get lost, or usually in very cold weather have them in those foot muff things in the car and in their pram. The people who came up to me in the supermarket etc. to talk to me as though I was an idiot got short shrift but usually backed off when it transpired that I was about 15 years old than they thought I was, and it wasn't my first baby. (Incidentally another of mine didn't like ever taking their socks off even when they needed a bath and had to have fresh ones on again afterwards - small children are very weird, I knew one who insisted on wearing shorts and wellies in all weathers for a while. Wise parents know when and how to pick their battles while keeping their kids safe and healthy.)
These young adults still run warmer than average, as do I, and we always have bare feet at home even on 'cold' floors, and get asked about our clothing choices by randomers, but we know when we are cold or might get cold (!!) and are sensible enough to take gloves and scarfs, and blankets/big coat in the car, even though most of the time we might not need them.
I would have thought that social workers would have a lot better to do than worry about this, and would also realise that alienating parents from social workers when they might need them in the future, by being nosy, judgy and talking nonsense (about the coat in car), might not be the best idea.