Don’t worry. It won’t snow in DC. It only barely snowed three times in the entire winter. It is NYC and Philly that you gotta worry about the snow. DC– too swampy for your typical Eastern winter.
Just layer up (I am from Southern California too and I was in a state of shock when it dropped below 60 degrees), and you will be fine.
A long-sleeve shirt, then a fleece or thick sweater, then finally an overcoat (for the rains or the winds… the sweater cannot stand up to the winds!). A cute scarf and a pair of gloves will help.
If you are going to stay indoors (e.g. at Gallaudet), they got heat on– to like 90 degrees (especially at Dawes!). So if you layer up, you can peel off those layers to cool off.
Be glad you didn’t come in January when it dropped below 30 degrees.