Daisy is right (of course, we have separately backpacked in very similar conditions). With temps down in the 40s or 30s F and windy, as normally happens in high mountain environments, you can't afford to get wet. Hypothermia happens really fast under such conditions.

Here's a hint for the "suck it up" method. If it stops raining long enough, and your clothing is made of synthetic materials, it will dry from your body heat in less than an hour. If this doesn't happen before bedtime (it usually doesn't), I take a large plastic bag, put my damp daytime clothing inside, seal it up and put it in the bottom of my sleeping bag. The clothing won't dry (you definitely don't want the moisture in your sleeping bag insulation), but in the morning it will be body temperature so you won't scream when you put it on! Plus, with the clothing already warmed to body temp, it will dry from your body heat that much faster.

Using an umbrella with trekking poles is not something I want to try to do, and I definitely can't hike without trekking poles. Plus fighting an umbrella in windy conditions is no fun, since I have no desire to play Mary Poppins.