The state of Florida has approved the Sunshine Protection Act which eliminates DST in Florida.
What changes do I need to make to my .NET code so that it won't get the answer wrong when converting UTC DateTime to Florida local time?
You don't need to make any code changes.
.Net gets its timezone information from Windows. Just update Windows. Microsoft will release an update before the law goes into effect.
The update will be listed here (credit to @HansPassant)