Here in Utah, I don't need a coggins to transport a horse inside the state. I do need a Coggins to cross state lines.
Various National Parks, ( Bryce Canyon, Zions, Yellowstone ) all require a coggins to enter the park. My state park do not.
Depending on the event. Different event organizer may or may not require coggins or current health certificates for horses coming to participate. We used to require current health papers for horses attending the Competitive Trail Ride that I sponsored and managed. It was just a rule I had so the other 100 horse owners were more comfortable bringing there horses to compete amongst so many other strange horses.
If you are just going on a trail ride with 3-4 friends and staying inside the state. You are probably OK., But check with your local state laws.