https://www.gamespot.com/articles/in-red-dead-redemption-2-you-can-lose-your-hat-and/1100-6461904/

Rockstar Games has confirmed another small but intriguing detail about Red Dead Redemption 2. We discovered in our preview recently that main character Arthur Morgan can lose his hat if he falls down hard enough. Thankfully, you can pick your hat back up. Or...you can pick up someone else's hat, like a true outlaw.

In the session I played, my hat fell off during a scuffle with lawmen. A sheriff also lost his hat in the battle. So I picked it up and put it on. I was intrigued to know if the authorities would treat me differently. They did not.