A few posters touched on the real issue in this thread, (Clarity). It is certainly not the law, the law is very clear. Drinking and operating a motor vehicle (golf carts) is wrong and a violation of the law, if you drink or are in possession of an open container with alcohol in your vehicle, you are violating the law. That is nothing new in Florida. 561 FS, 316.193, F.S. Local counties and municipalities have even tighter ordinances addressing alcohol consumption in public. (Lady Lakes)
The fogginess to many comes from being allowed to drink in the square and walk around the business area of the square with an alcoholic beverage. You are not being allowed to leave a business selling alcohol with a beverage. Florida law prohibits any establishment selling alcohol to allow customers to leave the premises with an open beverage. Most establishments will have that posted near the exit for clarification. A local governing body can designate through permitting a "Wet Zone" for the consumption of alcohol.
I would recommend those managing the squares post signs designating "Wet Zones (alcohol consumption permitted) along the perimeters of where it is permissible to consume alcohol. That will make violations enforceable and also give Villagers clarity on where you can and cannot consume alcohol.
If you went to see an attorney about the consumption issue with golf carts, he would probably advise the following: Bring your beverages and a lawn chair. Set up your lawn chair in front of your golf cart and pour/consume your beverages while in the lawn chair, not in the cart. It is a good bet you will not be cited for a violation. I'm just saying