Thousands of people gathered in downtown D.C. on Saturday afternoon. They ordered hot chocolate, sang along to the blaring holiday music and laughed loudly. But for a moment, they fell utterly quiet.

When Gerren Price told his then-girlfriend he was taking her to the National Mistletoe, she was skeptical. She had heard of their other plans: the DowntownDC Holiday Market, the U.S. Botanic Garden’s ...