The question does not really make sense. CSS is applied to any HTML elements. So, it can be applied to any controls, or not control, any elements. And there is no such HTML element as "composite custom user control". As you tag is "C# 4.0", it probably means that you are using ASP.NET in one or another form, and it simply means that your code renders some HTML, and your "composite custom user control" is translated in HTTP response as some HTML. Look at this HTML and see what's there. And apply CSS to whatever you want.
If something is unclear here, it would mean that you would need start learning what Web does, pretty much from scratch, but anyway, your follow-up questions will be welcome.
See also:
https://msdn.microsoft.com/en-us/library/h4kete56.aspx[
^],
http://www.wiseowl.co.uk/blog/s253/css-style-sheets.htm[
^],
http://www.aspnettutorials.com/tutorials/themes/usingcss-csharp[
^].
—SA