There was a lot of mining activity on Montana back in the day, so gravel access roads crisscross the landscape. Now, you probably cringe reading that, but the roads have come to resemble graded trails that happen to be extra wide. It also means that any portion of this alpine is accessible - especially by mtn. bike.
The approach drive does most of the elevation gain for you, so you are free to explore the alpine. The very beginning of the trail is a sketchy route across a landslide, but it's smooth sailing after that. The recommended trail heads to the glacier and small basin at the base of one of Montana's many peaks.
After switchbacking somewhat along the main approach road, you will come to a three-way intersection. The left trail takes you all the way around the plateau (about 21km) the right trail dips into the valley on your right, climbs to the ridge and can be used to summit the peak situated at 2 o'clock.
The middle trail is the one you want, however, as it takes you to the pass straight ahead (3km), across a bit of a rocky moonscape, and winds to the basin/glacier at the foot of Montana proper.
Trails are impossible to lose as long as the ground is snow free (though remember which fork you took at each split) and the slight elevation gain is along moderately graded pathways. I really liked this trail for two reasons: 1, the lack of trees and plateau-like landscape makes trails optional 2 - seeing wild groups of caribou skipping across the meadows.
Carcross visitor center has a great map of Montana mountain (though the directions on the page led me up the wrong trail - stay STRAIGHT at the 3-way!)
If that's closed, just take the highway south just over the bridge. Take the first road on the right to find yourself in a small residential cul de sac - on the left you will see a rough gravel road heading straight up the mountain, warning 4wd required.
They weren't kidding. There are some BIG rocks and awkward washouts. High clearance a must. It is 9km to the trailhead, but at about the 7km mark there is a large turn-out and possible camp area where some people give their trucks a break. 2km later there is a massive landslide that is the clear end of the road and beginning of the trail proper.
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