Since it was coming from a wooded area, I suspect it had just laid eggs and was heading back....
See my comment about snappers and handling them. I used to do exactly what you did till I read about the potential for backbone damage by carrying them that way.
Every time I see a snapper I feel kind of like I’m looking at something from the Cretaceous Period. They are neat little critters. They can make interesting “pets”. I “trained” one to come and eat fish from my hand - LONG FISH _ by slapping the side of his pool. When he heard it, he would come swimming and get the trash fish I got for him.