You could consider putting him in the car without it. He'll be very cold in about 2 minutes. You'd have to be willing to stop the car and then put the jacket on, but you're hassled as it is so it wouldn't be much more.
Don't let anyone tell you that kids get sick from being cold. They don't. Short of frostbite after a few hours in the elements, there's no harm in a brief period of cold! They get sick from being indoors all the time with germs that flourish in the dry heat!!
Anyway, if you take the fight out of the situation, and then calmly tell him "Gee, I'm nice and warm because I'm wearing my jacket." He'll say he's cold, and you say, "How sad for you. I'M nice and warm because I'M wearing my nice warm jacket. I LOVE my warm jacket." Just be repetitive and it will work. Don't yell over his screaming - just wait until he calms down or takes a breath. (This is a trick I learned from a teacher who dealt with kids who didn't want to wear their gloves at recess. They were too cold to play so they had to stand around with their hands in their pockets. They got real tired of it, and after 2 days of not playing, they wore their mittens! (She did not let them go back in the building for mittens - she couldn't even if she wanted to because she had to be watching the other kids. They kept their hands in their pockets or pulled up in their sleeves.)
Your son is being stubborn and that's normal for a 3 year old. You are letting it get you all upset and affect your life - that means he's running the show and I know you don't want that. It's a battle of wills and you are the parent. You can't out-scream him, but you can outlast him!