This is a non-trivial, if not impossible task to accomplish with the wmp control in winforms.
I don't know of any way to actually draw on the wmp but you could draw on a transparent panel overlaid over the wmp. This will not work will the video is playing but you can show the drawing while it is paused. I have used this technique to draw over a 3rd party video control that works similarly to wmp.(Edit - this does not seem to work with the wmp control)
However, as real transparent panels are also rather tricky in winforms, another way would be to grab an image from the video and draw on the overlaid image. Again, only when it is paused.
This commercial control does enable drawing over the video. It has an event that fires every frame that you can use to do the drawing. The big downside, though is that you can't really do anything too fancy as your drawing routine needs to finish before the next frame is drawn.
I would strongly encourage you to use WPF(even if its a wpf control hosted within a winforms app) to show your video. It is a whole lot easier to draw on video(including playing video) in wpf.
EDIT
I just tested drawing over the wmp using a transparent panel and its doesn't behave as my 3rd party control did,so I suggest you do the video playing bit in WPF and host that in your winforms app. (I just tested that too using @Callums inkcanvas suggestion and it works like a charm)