In order to do what you want to do using a C# program you would need some kind of library to automate the browser. This is possible with IE using WATIN, which is really a testing library, but can do this sort of thing. For example,
using WatiN.Core;
...
foreach (IE ie in IE.InternetExplorers())
{
Console.Out.WriteLine(ie.Html);
}
This code snippet is IE specific but version 2.0 (in beta) also works with Firefox. The roadmap does mention support for Chrome but I don't think its implemented yet.
You could also try Selenium, another testing library. It supports all the major browsers though it may be a little more complicated to set up.