I was under the impression they were not, because of the following story:
“In 1878 a shipwrecked cargo of coconuts was washed onto the barren, sandy beach and took root. Early settlers also gathered the nuts and planted them to create a palm-shaded haven, which was named Palm City in 1880. Renamed Palm Beach in 1887, it developed as a resort after Henry Flagler extended the Florida East Coast Railroad to West Palm Beach in 1894 and opened his Royal Poinciana Hotel. “
But with a little more thought, I realized this does not necessarily mean there were absolutely no palm trees before this, it could be that there were a few around but this event made them really take off. And, the story only references the Palm Beach area, and not all of Florida.
Anybody know the straight dope?