Running warms you up the equivalent of about 20°F, so when you're planning what to wear, look at how warm it will be when you finish and dress for that, and then add layers for the start temperature. Time matters, so short runs of around 30 minutes need a few more layers since you won't have time to warm up before you're finishing your run. 

55°F is considered the optimal temperature for racing since your body isn't using excess energy to warm you up or cool you down. When it is cold, try to shed layers before you start sweating so the remaining layers don't make you colder. Some runner's extremities can get cold - so they are comfortable in shorts and a short sleeve as long as they have gloves and their ears covered. This graphic below is a guide if you unsure know where to start adjusting for cooler temperatures.

Rain running
In Florida we can run in the rain because it's warmer - running in the rain can be really invigorating and splashing through puddles can make you feel like a kid. There are a few conditions you'll want to be careful with: avoid running during thunderstorms due to the risk of being struck by lightning (Florida scores first place in lightning density among all 50 U.S. states, with 285 lightning events per square mile), or when the rain + temperature + wind puts you at a risk for hypothermia.

Wear a brimmed hat to keep rain out of your eyes. Jackets that keep rain out also keep sweat in so you're bound to get wet either way - if it's prior to a race, just bundle up inside a big lawn trash bag or throwaway poncho - just as effective as any expensive running rain jacket. You can put a layer of vaseline or aquaphor on your feet to help prevent blisters. Wear snug fitting clothing and be sure to apply an antichafe product. Be mindful of where you step - painted road stripes, leaves, or even deep puddles can be slip and fall hazards.