What are the weather conditions in Cuba (and Florida) in January/February/March ?
Some statistics etc would be useful.
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In short, the weather is great, especially towards the end of that period. The hurricane season is over (it lasts until mid November or so), and it's not extremely hot & humid like it can be in the summer.
In Havana, average max temperatures are between 26 and 28 °C (79-82 °F), while average min temperatures are 19-20 °C (66-68 °F). See e.g. this chart in Wikipedia for details. March and April are the months with the least rainfall in Cuba; January and February may see a bit more rain, but most of the time the weather is pleasant.
I guess it depends where you are from. For Cubans, February is considered the coldest month of the year, and you will not see many Cubans in a beach during this period. However if you are coming from a country with a "real winter", it will probably be a paradise for you. If you plan visiting a beach in the north shore near Havana City, or doing some scuba diving, you will have to be careful with Portuguese Man o' Wars, which are more common during this period than in summer in that region.
By the way, mentioning Cuba and Florida in the same sentence as if they were the same thing may give you some troubles in either of those two places :D