If you take it without a title and later find out it is stolen you could get in trouble. You would have broken the law.
The state of Florida has some laws that will allow you to get a "provisional" title for an abandoned trailer using a bill of sale from the owner of the land where it is abandoned, if the owner of the trailer is unknown. If the actual owner of the trailer claims ownership after you have paid, you can loose the trailer and your money. I found this out a few years ago when I found one I thought I might restore. I saw an old trailer in FL setting beside the road and the land owner did not know from whom or where it came from. It was there when they bought the property. I did not get it, since I did not want the take the risk/cost to transport it home, 700 miles.
My opinion; for a few hundred bucks it may be worth the risk to get it in your possession, legally.
You can find how to do this online pretty easily. You will need a notarized bill of sale and the VIN when you go for the provisional title.
Search here - Official Website Florida Department of Highway Safety and Motor Vehicles
edit: If there is an old FL annual sticker on the window or an old license plate on it you may be able to find the previous owner's name using those. When you re-title it you may have to pay back taxes that are owed before a new title is issued.