I spent my childhood using port-o-potties during summer athletic events/tournaments, with weather that was above 105F. In the winter, I played on travel sports teams that practiced in places that had no other bathroom facility except port-o-potties. Sometimes the weather was around 32F during those winter mornings. So, yeah, I guess I’m saying you’ll survive it.
Another alternative is to build single stall bathrooms that have a door which opens into the main hallway of the school. Many schools have already built these for faculty use. It’s just a small room that contains one toilet, one sink, and has ac/heat for climate control. They would need an entire wing of these for student use, to accommodate everyone, but at least there wouldn’t be a large open room for students to congregate and cause fights. No one is going to be beating another student’s head against a sink, or the floor, in a single occupant bathroom.