You could probably argue that in a technical sense but it's a person who works with HTML/CSS but not say JS etc would probably be considered a designer more than a programmer.

I've worked at a bunch of different companies (Yahoo!, The Guardian, various smaller companies) and in all of them the "designers" were the people who did the visual design using Photoshop and Illustrator - those people rarely if ever wrote HTML and CSS, and almost never to production level standards.

The people writing production-ready HTML and CSS were known as "web developers" or "client-side/front-end engineers".