Children learn from what they get use to. If you are a family who sit round the table for dinner, then that is 'normal', if you sit around the t.v., that becomes 'normal'.
If you do the zip up for her, she will think that that it 'normal', if you leave her to do it, she will have to decide for herself, whether she wants to be cold or not, either way she will be fine.
If you want her to hold your hand when you cross the road, then hold her hand, be calm and consistent, it becomes 'normal'.
Good luck, greater challenges ahead, sorry but very true!