As the others have stated the best chance at one of Skagit wild steelhead is during the spring CnR season. The best period is typically mid-April though that varies from year to year depending on the water conditions (I can remember a year or two where April was a nearly complete washout.
However if you goal is show your fly to a BIIIG one I would recommend the last 2 weeks of February. It is my opinion that will provide your best shot at one of Skagit finest - a fish that would be a "pig" in anyone's book. In terms of catch rates late February is the pits but for a given period of time your odds of hooking up with one of the big boys is the greatest of anytime of the year.
The first decent push of wild fish typically occurs at that time of the year with many of those fish being what some call the dominate males. They are fresh fish at their very best and more importantly they are moving fish. This makes agressive and reachable for the fly angler. I would target any of the water downstream of the Sauk.
Expect to spend long hours/days between fish but that one could be "AWESOME BABY".