I have a stubborn waker-upper, and at times tough to get going in the morning 10 year old. I've been through the yelling and threatening (when she was around 4-6), and all it does is cause her to have an anxiety meltdown, making matters SO much worse! No matter what, I have to keep my demeanor easy going if she is starting to make bad choices, and let natural consequences rule. I have a few different suggestions based on what works for us.
Give him control of his wake up time. Get him and alarm clock and teach him how to use it. Make it fun. Ask him to think about what time he needs to be up in order to comfortably get ready for school and not be late. Try to steer the conversation towards a reasonable time if you think he is off base. If he is up early and fully ready to walk out the door for school, his reward is a little TV time or Ipad time, or whatever he likes to play with in his free time.
If he is refusing to eat, no TV time or toys before school. And stick a granola bar in his backpack or something. I do make it a point to have favorite cereals, outmeals, frozen waffles, etc on hand, things I know my girls like and can prepare themselves. I offer to make eggs if they will eat them. Sometimes I make muffins.
One thing my 10 year old loves to do is take a shower in the morning. Your son may be a little young to shower on his own, but she is a groggy, cranky mess coming out bed, and after her shower, she is a new kid! She hates being cold after getting out of bed, and getting a hot shower really helps.
Unless it's dangerously cold, I wouldn't force the coat on either. Stuff it in his backpack if he won't put it on, or even let him go without it. He will learn it isn't very comfortable, or the adults at school will get after him he needs to be dressed properly to go out for recess. I think the most important thing is to remain calm,with just a gentle reminder "it's 8:30, the time we need to be leaving to be at school on time" and if he dawdles, let him be tardy. Don't even say anything about it if his dawdling causes you to leave late. Pretend nothing is wrong, be cheerful. I learned that a lot of times, you aren't really going to be late if you leave 3-5 minutes past your target time, and it's not worth pressuring him about it. If you truly do become late, he will have to tell the adults in school why he was late HONESTLY. I know my DD would be mortified if I had to tell the school adults she was late due to her own poor time management this morning. She's often yelling about not wanting to go to school (over some minor issue). Probably trying to engage me in an argument, or get her way about something I've said no to. I just ignore any "I don't want to go to school, or I'm not going to school" remarks. Happens all the time. She always goes anyway.
If he has a bad morning, discuss it calmly after school. I talk to my DD with empathy for her stress, and what she can do differently to have a better morning next time. Sometimes it is setting the alarm clock earlier. Often times, picking out clothes the night before helps too. Hang in there. There's something to learn from every "bad" morning. I've learned a lot to let go of my own control issues, and let natural consequences rule.