My band teacher lets us take off our coats and shakos in the stands during football games for health and safety reasons. Your director may not allow it or you may disagree with this policy. That is perfectly fine unless wearing unnecessary layers is posing a health hazard to the ensemble. We are allowed to not have our coats and shakos on both before and after we perform as a marching band.
As mentioned before, my band teacher is primarily concerned about our safety rather than our appearance. Wearing excess clothing in 90 degree (Fahrenheit system) weather leads, not only to discomfort and lowered morale, but to serious health issues. The symptoms of heat exhaustion are confusion, fatigue, headache, dark-colored urine, fainting, headache, muscle and abdominal cramps, nausea, vomiting, diarrhea, pale skin, profuse sweating, and rapid heartbeat. The symptoms of heatstroke are a core body temperature over 105 degrees, nausea, seizures, confusion, rapid, sometimes weak heartbeat, rapid, shallow breathing, disorientation, and sometimes loss of consciousness or coma. (But you don't let anyone get to that point, right? RIGHT?!)
Taking off the jackets detracts somewhat from our appearance. So does irritability from heat exhaustion. You might worry about dirt stains on the band uniforms. Well, would you rather have vomit stains? Sometimes, things just happen, but heat illness is VERY preventable if you are willing to make a few small sacrifices. If you notice that a band member is more irritable than usual, encourage them to unzip and get them a sports drink or Pedialyte (Water will worsen salt depletion.). Alert the director or a section leader of what is going on.
I am not a doctor. I am just a concerned student. Safety is the first step to a fluteiful performance. If you are concerned about your band's performance in the stands on hot days, please PLEASE allow them to unzip. Try establishing a "temperature policy." For example, allow the band to take off their coats and shakos in the stands when the temperature is consistently 95˚F. Allow them to take off their jacket if they are feeling the symptoms of heat exhaustion. Demanding a certain appearance is, to a degree, necessary for performance, but it should never come at the expense of students' health.