Does playing a brass instrument like a trumpet or trombone puff your cheeks or make them bigger?

NO, but...: You constantly use your cheeks and facial muscles to play those instruments, but just like playing the drums does not make your fingers that hold the sticks bigger, your cheeks have natural stretching ability just as when you blow out the candles on your cake, and they will return to their normal size when done.

No: No. What you have observed is a technique which some players have learned how to use in order to hold or sustain a note for a long period of time. They store air in their mouths by expanding their cheeks outward. This is not required however for standard operaion of the instrument, it is just one particular technique some have mastered.