There is a considerable environmental difference that will affect every instrument differently. You have to tune outdoors to perform outdoors. The trick here is to train your students to use tuners and buddy system it. Hold for the other, and then check the other. Unless you are lucky and have contest in 70-72 degree temps outside I would never leave it alone with just indoor tuning.

It’s part of why I do not like indoor warmups for marching band contests.