To take DD home from playground because she wouldn't do her coat up

[Toomuchtooyoung01]

DD 3.5yrs refusing to let me do her coat up as she wanted to show everyone in the playground her new dress. (Several people had commented on it on our way in).
After several times telling her that I needed to do her coat up and explaining why (because its cold) and her refusing, I said we were going home (again, explained lots of times we would go home if she wouldnt do her coat up).
DD hysterically crying all the way back to the car and back home.
Am I out of order for taking her home?

PS: The op hasn't been back to tell us but from reading both of her two posts, it sounds as though her daughter stayed at home. I don't see the point of that for such a minor issue.