That's not a watermark. It's a "placeholder". ASP.NET controls are not some special thing that browsers handle. ASP.NET markup,
<asp...
tags, just tell the view engine to emit normal HTML.
Now, there is no standard way of adding a placeholder to a dropdown list. It's just not in the HTML spec. You can fake it, but it's not going to work how you're probably imagining it. On top of that, placeholder support isn't standard across all browsers or browser versions.
You can find an example
here[
^]. You're probably going to have to do some fudging in ASP.NET to emit the correct HTML, like
this[
^].