Map from Google - Florida

In much of Florida the climate is sub-tropical, with mild winters (but subject to short cold spells) and hot and sunny summers, from June to September, which are also muggy and with frequent thunderstorms. In the far south, where Miami is located, the climate becomes tropical, since the January average temperature reaches 68 °F. In summer and early autumn, Florida is prone to hurricanes.

The summer temperature are uniform from north to south, especially in the daytime, since highs range between 88 and 91 °F, while at night they become warmer as you head south, in fact they go from 70 °F in the far north, to 81 °F in the Keys. On the contrary, winter temperatures are very different: in January the daily average goes from 52 °F in the north (therefore it's similar to that of many Mediterranean areas) to 68 °F in the far south. In summer it's especially the high humidity that makes the heat annoying, even though periods of intense heat are possible, with highs about 99/100 °F. Afternoon breezes and thunderstorms give a bit of relief, otherwise to cool off you can swim in the sea, or take refuge in air conditioned buildings.
In winter there are on average 8/9 days with rain in the north, and 6/7 in the center-south. The rains are due to frontal systems, which are formed because of the clash of air masses, and may be accompanied by wind, and sometimes by cold air. The rare cold spells can occur from late November to mid-March.
In the northern part of Florida, snow is rare but sometimes can occur; in the central part (see Orlando) it becomes very rare, while in the south, which includes Miami, it practically never occurs.
On winter nights, fog may form in the north.

Here are the average minimum and maximum temperatures of January in some locations.

Average temperatures in January in Florida

In summer the weather is often sunny, but also some cloudiness can form, more or less extended, which can lead to thunderstorms, sometimes accompanied by wind gusts, and less frequently by hail. Fortunately, these thunderstorms do not last long and soon give way to the sun.
Tornados in Florida are more common than in the Great Plains and the Midwest of the United States, but are generally much less intense. Sometimes, particularly intense tornados can occur in winter or spring, due to abrupt intrusions of cold air.
The season of hurricanes and tropical storms goes from June to November, although they are more likely from August to October. A particularly intense hurricane that hit Florida has been the Labor Day hurricane, in August-September 1935. The areas most at risk are the coastal ones, due to storm surges from the sea.
The amount of sunshine in Florida is very good all year round: in fact, the state nickname is "Sunshine State". The relatively sunnier months are March and April in the south, and April and May in the north, while the least sunny season is winter, when however the sun often shines. In summer, as mentioned, the sky is not always clear: scattered clouds can form, and sometimes they can grow until they give rise to showers and thunderstorms, then the sun will come back.

Now let's see in detail the climate of some cities, starting from the north.

In Pensacola, located in the northwest, overlooking the Gulf of Mexico, the average temperature goes from 52 °F in January, to 82.5 °F in July. Therefore, winter is not so mild, and besides short cold spells are possible, and sometimes even frosts. The coldest record is even 5 °F, recorded in January 1985. Rainfall amounts to 65 inches per year, and is quite abundant in winter, as it always exceeds on average 4 inches per month, while there are two relative breaks in spring and autumn, in April-May and October-November (although particularly heavy rains can sometimes occur even in these periods). This is due to clashes of air masses, which generate disturbances, which transfer mild and moist air from the Gulf of Mexico.
Here is the average precipitation.
Average precipitation Pensacola
Pensacola J F M A M J J A S O N D Year
Prec. (in) 4.6 5.1 5.8 4.3 4.1 6.6 7.4 6.8 6.0 5.2 4.7 4.6 65.3
Days 9 9 8 7 7 11 14 14 9 6 7 9 110

Pensacola was hit by Hurricane Ivan in September 2004, along with the neighboring state of Alabama, while it was only touched by Hurricane Katrina a year later.
Here are the average temperatures of Pensacola.
Pensacola average temperatures
Pensacola J F M A M J J A S O N D
Min (°F) 42 46 51 58 66 73 74 74 70 60 51 44
Max (°F) 60 64 70 76 83 89 90 89 87 79 70 63

In the other northern cities (see Tallahassee, Jacksonville), the climate is similar to that of Pensacola.

Continuing to the south, we arrive in Orlando, at the center of the peninsula, where also Disneyworld is located. Here winter is already much milder, given that the January average rises to 60 °F. However, even here sometimes short cold spells with slight frosts are possible, from November to March. Every so often even snow can fall, although the only event with accumulation in the city occurred in 1948, and in the outskirts also in 1977.
In Orlando, as generally in south-central Florida, winter is the least rainy season, so that 2.2 to 2.6 in of rain per month fall from November to February. Summer is, as usual, the rainiest season, because of thunderstorms, but also of the contribution given by hurricanes: rainfall exceeds 6 inches per month from June to September. Here is the average precipitation.
Average precipitation Orlando
Orlando J F M A M J J A S O N D Year
Prec. (in) 2.4 2.4 3.8 2.7 3.5 7.6 7.3 7.1 6.0 3.3 2.2 2.6 50.7
Days 7 7 7 6 8 16 16 17 13 8 6 7 118

Here are the average temperatures.
Orlando average temperatures
Orlando J F M A M J J A S O N D
Min (°F) 49 52 56 60 66 72 74 74 73 66 59 52
Max (°F) 71 74 78 83 88 91 92 92 89 85 78 73

In Tampa, located on the west coast, south-west of Orlando, and in Bradenton, located south of Tampa, the climate is similar.

Further south, we enter an area where cold waves in winter are very rare, and in any case less intense, bringing merely a bit cold at night. In this area the climate can already be described as tropical. In West Palm Beach the average in January is 66 °F, and in Miami it reaches 68 °F.
Here are the average temperatures in Miami.
Miami average temperatures
Miami J F M A M J J A S O N D
Min (°F) 60 62 65 68 73 76 77 77 76 74 68 63
Max (°F) 76 78 80 83 87 89 91 91 89 86 82 78

South of Miami, in the Keys, the daytime temperatures are similar, but the minimum temperature is even higher: in Key West in January it's 64 °F, in July 79.5 °F.

Florida Keys

In the northernmost part of the Gulf of Mexico, the sea is warm enough for swimming from May to November, and becomes very warm from June to September, while in winter it is a bit cold, as you can see in the table regarding the sea temperatures in Pensacola.
Sea temperature Pensacola
Pensacola J F M A M J J A S O N D
Sea (°F) 64 64 66 70 75 82 84 84 82 77 73 68

On the northeast coast, the Atlantic Ocean is warmer in the winter months, so that it does not drop below 68 °F in February, as you can see from the sea temperatures in Fernandina Beach. To find similar temperatures on the West Coast, you have to go down to the latitude of Tampa.
Here are the average sea temperatures in Fernandina Beach.
Sea temperature Fernandina Beach
Fern. Beach J F M A M J J A S O N D
Sea (°F) 70 70 70 72 77 81 82 84 82 79 75 73

To find sea temperatures acceptable even in winter, about 73/75 °F, you have to go to the south on the west coast (see Marco Island), while on the east coast these temperatures are recorded already at Cape Canaveral. In Miami, in the south-east, the sea is just warmer than in Cape Canaveral.
Here are the average sea temperatures in Miami.
Sea temperature Miami
Miami J F M A M J J A S O N D
Sea (°F) 75 75 75 77 81 84 84 86 84 82 79 77

When to go

The best time to visit South Florida and Miami goes from December to April. In winter Miami is definitely the warmest and most sheltered place throughout the United States, and there are many sunny days, however, even here sometimes there can be a bit of wind, cool air and some rain. In the center-north, where the risk of cold and rain is larger, you can choose spring and autumn, ie, March and April, and October and November, although in October hurricanes are still possible.
For swimming, as we have seen the sea is warm enough in winter in the south, although the weather is not always ideal: sometimes it can be cool, and even a little cold: hence you can choose the period mid-March to late April. In May, the heat begins to be felt and thunderstorms become more frequent, but you can still go for beach life. Of course you could also go in the long summer, but the heat is sweltering, and there is also the risk of hurricanes.