our school does snack too... lunches span from 10:20 am to 1:40 pm... so they either snack in the morning or afternoon to make up for an odd lunch hour.
It's healthy snacks only too... and a peanut free school. As well, the teacher requests nothing messy or requiring a spoon (often eating on the fly)
My girls bring fresh fruit, nutrigrain bars, sun chips, fruit leather, cereal, granola bars, raisins, cheesy crackers, popcorn, string cheese. All that is considered healthy. They are in grade 1, 3, 5 and I keep a snack bucket within reach in the pantry. Whatever I buy (on sale) I add to the bucket. THEY pick their daily snack. We also keep a fruit bowl stocked on the counter. House rule is that I buy fruit at $1.00/lb or less... so we're always eating something seasonal.
My kids are good about self regulating. One day I had Kudos bars in the pantry box. One girl took them to school and was told "not allowed" so she stoppped packing it for snack herself. Good at self regulating... No tears or hissy fits. They just choose a more proper snack. And I don't have to fight battles with their teachers on their behalf
They also pack their own lunches. They follow my rule... one "protein" (lunchmeat, tuna, or almond butter sandwich or hard boiled egg) and only one "treat" (cookies, kudos bar, pudding,or potato chips, etc...) they can fill out the rest of their lunch as they see fit. (fruit cup, string cheese, carrots, whatever they find...

)
I guess I'm pretty lucky to have such responsible girls. I've brought them up this way, though. And I know if they make the choices (within my "guidelines") they will eat what they pack.
So I guess I don't see this a battle worth fighting with the teacher. Just pack a healthy snack and be done with it. Let kiddo pick it out from healthy options.
BTW... as my kids get into 3-5th grade +, "contracts" (for grades, homework, attendance, etc...) are becoming more frequent. I see it as a way to get students to take on more personal responsibility. (and I see that as a good thing!

)My kids and I sign contracts that agree to signing conduct cards, how to handle missed assignments, etc... all the time. Legally binding? No. But it says, "yes! We are on the same page. We understand the expectations in your class." I have yet to find one I find so objectionable that I refuse to sign or want to go toe to toe with the teacher. That's just me though....