I've given up the idea of having cold showers here. I'm told Denver water is cold, and Ottawa cold water is unpleasant. Here, however, the cold water is tepid at best and actually warms up after about four minutes in the water.
Which is to say, my extremities cool down enough that the water feels warm. I am uncertain if that is the point of the showers, but it seems to work.
Perhaps North Cascade showers will be cold enough to be unpleasant. I guess I'll find out in less than a week.