Well question one: why are you doing this? If it's a student project, to learn or for fun, then that's fine. If it's for something real that you plan to use, I'd go with a ready-made solution. (Either just using a web browser -- there are lots of small ones if you don't like FF/IE/Opera/Chrome/Safari or use a code library for C#).
Anyway, I'm not sure. Presumably you could figure out the coordinates on the screen of the rectangle (or rectangles if it splits across lines) that enclose the link. Then you could use the MouseMove or MouseHover events of the control to check if the mouse if in one of the link-rectangles and display the appropriate message on the status strip.
I suspect that solution would be non-trivial, but not impossible.
Anyone else have a better solution?
All advice is offered in good faith only. You are ultimately responsible for effects of your programs and the integrity of the machines they run on.