DS1 began to "assert" himself over clothes when he was 2. By assert, I mean lengthy, thrashing, screaming tantrums. By the time we had got to a stage of even considering wearing coats, my resolve had been worn down by getting the rest of the clothing on. That autumn, I bought him a lovely coat, deliberately choosing the one with fire engines, police cars and helicopters which surely he would love... did he heck! The coat was lugged around all winter, barely worn. Only when he was shivering and threatening to turn blue could the coat be put on to him. (He began to accept the coat the following year. DS2 has finally made the expenditure worthwhile)
He's still very exacting about what he will wear now that he's 6. He HATES trousers. Until the school uniform was clarified, we thought that he had to wear trousers most of the year. Every bloody morning was a battle to get his uniform on. Since we've found out that uniform shorts are acceptable all year, he's worn them, getting dressed with far less distress on all parts. He has long socks for the colder weather which to be honest gives the same coverage as a girl in a skirt and socks, yet psycologically the word "shorts" provokes some kind of reaction in people.
Now he's getting to an age of reasoning and logic, we can save the trousers/ shorts argument for the times that it is worth having, like cool evenings when camping, and because it's occasional and not forced on him there is more likely to be a positive outcome. When he was younger, he understood that sun = warm, and struggled to process that despite the winter sun glowing through his window, it could be perishingly cold outside.
He is a child who is happy and healthy (never missed a day off school), who doesn't feel the cold easily and is very stubborn. (He's also co-operative and reasonable about most other aspects of life)
The key thing for me is that the child has access to the coat. Pick your battles. A milder winter day, probably not worth the cost on the child and the siblings (late, stressed). In the playground when he's shivering, more worthwhile. Involving the child in buying a new coat that they like the look and feel of could help.
I can understand that the pressure of an ultra-resistant toddler and meeting the needs of the other siblings means that the coat is a battle that is one she is reluctant to tackle day after day.