Yes, I believe that Mike Huckabee moved to Florida to further his political career. The joke is that he was too well known for being a hypocrite in Arkansas state politics, so he had to move somewhere else to continue work in that field. The man thinks he can buy the presidency.
Mike Huckabee definitely moved to Florida to advance his political career. No former governor of Arkansas is going to win the White House anymore. Now, the GOP needs to win Florida and other big Southern states like Georgia and North Carolina in order to win the presidency. Florida's population is increasing every year, and Huckabee needs to win Florida to win the White House.
Whatever Huckabee's motivations are to move to Florida, furthering his political career is unlikely one of them. He has an expansive political base in home state of Arkansas and his brand of compassionate Christian-conservatism plays more there or in neighboring 'deep south' states than it would in Florida. Therefore it is more likely Huckabee moved to Florida for the sunshine, rather than politics.
I do not believe that Mike Huckabee moved to Florida to further his political career. This move was made a few years ago and shouldn't reflect anything at this point in time. Huckabee voiced this fact on CNN as people believed it was a political move for the 2012 elections.
No, I do not believe that Mike Huckabee moved to Florida to further his political career, because he likely moved to Florida just because that is where people move when they get old. In Florida, there is warm weather, there are condos, and there is Disney World. What old person wouldn't want to live there? Huckabee included.