They can be, just ask the people who did the expedition everest challenge this year.
Most races, Disney and otherwise, are only canceled if the weather is too dangerous to proceed. This could be lightning, torrential rain, a blizzard, or it gets too hot. A light or even medium to heavy rain won't cancel most events and neither will some snow (not that that is a worry so much for Disney). Like Chicago a couple of years ago a race may also be stopped if the temperatures get too high.
If you are speaking about the Marathon in January you probably don't have to worry. January in Florida is neither too hot nor too cold and it is rare it rains any harder than a spring shower up north.