Can an employer require a doctor's note with a diagnosis on it?
Perception is the issue here, I suspect. He may not notice the smokers. Maybe they are outside the building or otherwise not within his range of vision as much as you are when you eat your snacks.
If there are no hard and fast rules about breaks and your employer has written you up for snacking, did you and he have a meeting of the minds? That is, did he tell you what it is about your snacking that makes him so upset? Is it the time(s) of day that you snack (e.g., busiest time at the restaurant)? Is it the amount of time you take to consume your snacks? Is it the kind of snacks that you bring to work (e.g., messy, malodorous, from a competitor's eatery)?
Understanding his point of view might help you figure out a way to minimize his frustration with you and work out a compromise. It sounds to me as though you have told him that you are hypoglycemic--which may be true. But you don't really know, as you have not been diagnosed.
Maybe you should try telling your employer that you cannot afford the clinical testing necessary to provide him with a diagnosis; but you do know from life experience that you need a snack every two hours in order to feel energetic and focused--similar to smokers needing a cigarette every two hours. Ask him if you take no longer than five minutes twice a shift at agreed-upon times to snack, can he accommodate that?
The bottom line is that--depending to some degree on your state's employment laws--if you are not effective in your job, you can be fired. Asking for a doctor's note to substantiate your illness is really giving you a chance to be allowed to break or bend the rules to some degree.