Who wants it to be zipped - you or her? If she consistently puts on the jacket and makes no effort to try to zip it and instead comes to you whining for help, then you either a: teach her patiently to zip (buy a zipper at the fabric store and help her learn) or b: buy her a velcro-closing coat.
If it's you who's insisting that the coat be worn and the coat be zipped, perhaps you just need to let things be. She may be enjoying the drama she's created. "Hmmm, I don't put on my coat, mama gets all crazy, this is kind of fun".
Stop and evaluate this entire situation. How cold is the temperature? Does she run from the house to the bus in 10 seconds and then spends the day in school and the coat is a pain (doesn't fit in the locker, or is too bulky for where coats go? Does she hate the coat? Are you cold and therefore assume she's cold? Does she complain about being cold or seem comfortable? Will she wear a coat when it's snowing and sleeting and the temps are dangerously low? Will she wear a coat when she goes outside to play and a coat is appropriate for the temps and every other kid has a coat on?
Give some thought to the hill you're climbing up and assess, logically, whether this is an issue or not.