|Pale lilac gills and a rough stalk.|
|The cap is grainy, slightly translucent, brown with a hint of rose.|
This has been identified for me as Laccaria amethysteo-occidentalist. I couldn't find a common name: Amethyst Laccaria will have to do.
The younger mushrooms have a rosy, purple cap. As they mature, the cap turns brown. I picked one of the larger ones.
|The stem is slightly swollen at the base.|
The description of this mushroom on Mushroom Expert, and of its relatives in my Guide, demonstrate how difficult it is to identify any mushroom in the field.
Here's the cap, for example:
Cap: 1-7 cm; broadly convex, becoming nearly flat; often with a central depression; the margin even or inrolled, not lined or slightly lined when wet; nearly bald, or finely hairy-scaly; deep purple, soon fading to brown or buff. (Mushroom Expert)
So: it's convex or flat or concave; it's nearly bald, or hairy; it's lined or not, it's purple or brown or even buff. And so it goes. They're like snowflakes; no two are identical.*
What is usually a constant is the habitat. This one grows under conifers (check) west of the Rockies (check), and appears in colder weather (check).
When I had finished taking photographs, I replaced the mushroom in the moss, upright, so that it could deposit its spores without too much loss from its travels.
*Not exactly true. It depends on your definition of "identical". See: "Nano-snowflakes can be exactly alike."