T.C.
First, i wouldn't reinvent the wheel. If he is used to the sticker chart, and it works, whats the harm in adding a couple categories? 1. Get myself dressed... etc.
Second, don't make the coat a battle. Carry it to the car and let him feel the chill... he will likely ask for it.
I walked my daughter into her kindergarten class once in a short skirt, tank and sandals... in February, when it was in the teens outside... Just to tell her teacher "yes, I was aware of the temperature, and no, I wasnt a neglectful mother... i was prooving a point through natural consequences." This outfit was my daughter's favorite, and she wanted to wear it everyday. We fought over it everyday. No matter where I put it she found it and would put it on for school. On this morning I said nothing, but simply got in the car. At the end of the day she walked straight to her room, changed clothes, and then brought me her outfit and asked me to hide it real well and to give it back when it was warm weather.
The other thing i thought of was a cape. Maybe he likes superman... ? Buy or make him a cape he would WANT to wear... easy to wrap around him for short trips to and from the car. You can put fun pockets in it to hide little toys for the grocery store... (and some to stick a hat and gloves in) that would make bundleing up fun.
Last, I think he needs a visual chart for morning routine. Cut out pictures and paste them on a clockface made out of posterboard or in a checklist format. Have him work through it for stars or checks each morning. Prep him the nigh before..."when I wake you tomorrow morning I need to see you...." Let HIM tell you all the things that have to be done before school...go over the list together before bed each night for a few weeks. You might not think he would remmber, but in the morning, you can hand him his list or remind him to look at it. Laminate it and give him a crayon to check off.... give him control of getting himself ready.