My son got a bit picky around three. I didn't make a big deal of it. He got on some PBS Kids game that taught him all about nutrition. I think it was called Prof. Fizzy's Lunch Lab. He got his "gifted" on when it came to nutrition. He wasn't even four when he said "Dad, you already had one donut. Those are loaded with transfats that will clog your arteries! Please Dad, eat those only in moderation.".
He has moved on, but on most days he can still tell you what he has eaten, what food groups everything goes in and whether he should have more of something to balance his diet. So there you have it! Relaxed parenting and video games solved it.
I get that this wouldn't work with everyone. My husband has food texture issues and will vomit it he eats a long list of veggies.
One thing we've worked on is being nice about refusing food and finding something thing to eat. Like just quietly picking off the pepperonis instead of going on and on about how nasty they are.
