I know the area is equestrian heavy, but where would a beginner go to learn to ride in Washington?

I've heard of Kildare Stables in Millbrook, which supposedly offers horseback riding lessons and training to folks at any stage, so I'd figure that includes beginners. I don't know what the costs involved are; you'd have to inquire.

You're right, it is an equestrian-heavy area, so even a simple Google search will probably turn up more.