A light to medium rain doesn't affect trout fishing too much in general, as the trout aren't getting any wetter. You can even have some good midge and BWO hatches during a winter rain (not sure if this is true or matters at Accotink). And you actually have some advantage as trout won't spook as easily with the surface of the water distorting their view of you, but no reason to use a different fly than you would otherwise.
For heavier rains where run off can make the water color tainted, your intuition of moving to bigger, brighter streamers is probably a good idea.
Dalton