Is this REALLY a battle you want to fight? Is the kid smart enough to know he will be cold if he doesn't wear a coat, and to put one on if he is cold? It is a battle I flat out, ten thousand percent refused to even discuss (esp with my parents who did a LOT to give me great grief because Wiz hated coats) because if my kid wasn't smart enough to put a coat on when he got cold then he could freeze. If school wouldn't let him go out to recess if he had no coat, it was NOT MY PROBLEM. I was not cold. As long as difficult child owns a coat I would opt out of this battle.
There were entire YEARS when Wiz' coats were only worn 3-4 times because he just wasn't cold. I DID, and DO have a very firm policy that if you are cold because you neglected to bring your coat/jacket/gloves/hat/zebra you are NOT allowed to utter any words mentioning this in my presence. Period. Children who DO complain in my presence find that they are missing some very interesting, fun and "essential" things AND I follow them around complaining about everything I can think of (in a whine) for twice the amt of time I had to listen to them.
It even cured husband of this.
on the other hand, you can always do what my mom did. She made the thermometer the "bad guy". She used to make us listen to the weather reports, but you can use any thermometer or the weather channel or whatever. We couldn't go swimming or play in the hose in the summer until we had three days in a row that were 72 degrees or higher. We had to wear coats if it was snowing or some other temp outside. I cannot remember the coat rule because as a kid I was always cold, so I usually had a coat with me.
The rules were carved in stone. Totally out of her hands, or so we were led to believe. It is what it is kind of thing. Saved her eons of arguing because she would tell us to take it up with the weatherman or thermometer and then she would go on about her business. Fussing and whining earned chores that HAD to be done. I would designate ONE temperature source (tv station, indoor/outdoor thermometer, etc...) so that you don't end up with bickering over a couple of degrees because one station recorded the temp at another place than some other station.
This method will work ONLY as long as you are as close to 100% consistent with it. Write the rules out, post them by the thermometer or coat rack or wherever. If difficult child wants to argue, you walk away asfter telling him something like, "It sure is tough when the rules won't let you do what you want, isn't it?" and when he wants to negotiate let him argue it out - with the weather channel or thermometer. Remove his audience.
The second method (thermometer as bad guy) has worked really well with many kids I know. The ones who have the most problems are those with lots of sensory problems. For a kid with sensory problems relating to heat nad cold, the rules regarding coats, etc... can be brutal. The older I get the more I think that we need to pay a LOT more attention to sensory problems like this.
I do keep a bag with gloves, hats, scarfs, etc... in the car AND if we are going more than ten minutes away the kids have to bring their coats. They don't have to wear them, but they must bring them in case we have a breakdown or accident. When they were littler I kept a couple of extra jackets from thrift stores for each of them so that one could live in the car.
(We were always pretty sure we were on her last nerve when she would ask one of us to take out the trash or something, lol!)