I have been running an outside airline to my skimmer for a few years now, but without the scrubber. During the spring, summer, and fall it is never an issue with the temp. During the Winter however I can see a noticeable difference in how long my heaters have to run. To make up for this I just use bigger heaters than I normally would.
I live in WV where our winter temps are commonly in the teens and sometimes single digits. Living in FL I doubt you will have any temp problems, unless your tank is already close to needing a chiller.