Sam -
As Preston mentioned in my home area (north Puget Sound) the sea-runs do in fact enter the rivers in summer (as early late June or early July) and on into the late fall. In the south Sound where most of the fish use those smaller independent streams for rearing and spawning the fish tend to hang out in the salt until ready to spawn and then make the mad dash to the spawning areas. REgardless fish of either strategy spawn from early January through May with a normal peak sometime in mid-March with considerable year to year variation depending on stream flows and temperatures.
However back to the fish of the larger rivers in North Sound. While the timing of the cutthroat's return to the river is similar I like Preston find little evidence that they do so fed on salmon eggs. While it is not all that uncommon to see some cutthroat behind spawning salmon most do not do so. A well fished fly or nightcrawler will out fish salmon eggs by a wide margin in most cases.
While it is commonly believed by many anglers that the sea-run cutthroat run up into the smaller creeks with the fall/winter rains it has been my experience that many do not do so. Certainly there is some movement upstream towards spawning tributaries with the fall rains and even into some the larger tributaries. However I find that many do remain in mainstem areas until they are actually ready to spawn. However with the higher winter flows it is very difficult to get at the fish. Whenever I have found winter flows at levels similar to what I fish in the fall I can catch reasonable numbers of sea-runs (at least through February).
Tight lines
Curt