We just did DC, the first week of May, (Wonderful Park!!!) and if you are aware of the big cold-spell that hit... Even FL was cloudy and cool! Do not underestimate how freezing coolish weather can feel when you are wet. Man was I glad when the sun came out and it warmed up later in the day!!!
You can see a bit of a trip report on the thread about 'when to arrive'
For me, for that kind of $$$, I would want to be warm and comfortable to enjoy it. But, of course, it's all up to you!!!
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