You reminded me of being in DC on a family holiday about 12 years ago. I was 12 myself, it was about 100 degrees and 99% humidity so my siblings and I decided it would be an idea to have an ice fight on the steps of the Lincoln Memorial (we're Australian - we'll disrespect anything!) That was until we clean hit a tour guide in the back of the head with a huge chunk of ice, who then proceeded to chase us, shouting expletives.
And that's my favourite memory of Washington. I hope you're having a blast!