Judge Rodney Price told local news channel KFDM that the man had ignored signs about alligators in the water.
He "made the ill-considered decision to go into the water," Price said. "Someone shouted a warning, and he said 'f*** the alligators,' and thereupon jumped into the water and almost immediately yelled for help."
A witness who came running when she heard screams said she saw the huge reptile attack Woodward.
"I asked him please do not go swimming, there's a bigger alligator out here, please stay out of the water," a tearful Michelle Wright told KFDM. "The next thing I know, this girl is screaming: 'An alligator has got him, an alligator has got him'."
Woodward's body later was found with puncture wounds to his upper chest and left arm. Police said an autopsy is pending.