Bentley-
The issue in fishing the high lakes and what rod one needs is more of a matter of what you can comfortably cast and cover water with than the size of the fish you are likely to catch. The isn't a trout in Washington alpine lakes that a skill angler can not handle on a 3 weight.

However assuming you will be fishing from the shore and at least some days be dealing with wind a 5 or even a 6 weight would be a much better tool. Even more important than the line weight would be the rod length and type of line. I would look for a rod at least 8 1/2 feet or 9 feet long and for a main line I would have a weight forward floating line and for a second line I would go with a full sinking weight forward line with 3 sink rate. With the potential of some spooky fish (especially later in the season) learn to complete your cast with those weight forward lines 18 inches or so above the water's surface - that will provide a better presentation.

The longer rod and weight forward lines will allow you to clear some of the brush behind you and shot a fair of amount of line on the forward cast. Even though a weight forward is not the best line for roll casting it will be will worth your time to master the ability to make 50 foot roll casts. I think that you will find that the slow sinking line is golden at lot more than you would think. Getting the line below the surface of the lake on those still days can dramatically increase your strikes and will provide the ability to get deeper if needed.

Regarding flies - hands down my most successful flies in the alpine lakes were soft hackles with a dark olive being the best color. If I had to pick one size for the soft hackles it would a #12; a size #12 dark olive solf hackle fished on that slow sinking line has produced for me from ice out to ice up. In addition to a variety of soft hackles in several colors (brown, grey, and black) a few woolly buggers, chironomids, hare's ears, and copper Johns would be a good starting point for sub surface flies. Adams, elk hair caddis, a couple ants, humpies (red and yellow) and royal coachmen in sizes from 16 to 12 will provide the basics for the dry flies.

Tight lines
Curt