Yeah, I noticed that, it is different to have the Former Monarch placed ahead of her Successor, the now New Monarch.
As for Mary not wearing a coat, I think it's such a short distance from the car to the entrance, that she can tolerate the weather. I've noticed that she rarely wears a coat/stole to formal events also. Many of the Royal women wear formal coats over their gowns, Mary usually enters without a coat over her gown. I think for the same reason. I agree, it could be that she doesn't like wearing a bulky coat. I know how that goes, but with the extreme cold we've had, the car takes forever to warm up even in an attached garage plus if there's car trouble no one wants to get caught out in below zero temps. So I grit my teeth and put it on.
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