This route offers peace and quiet, solitude, and a steady trail climb up through an unspoiled Colorado forest. If you are looking for the easiest route to climb Mount White, however, this is not it. If you are looking for easy, consider an ascent from the west side, like up one of the roads.
Based on photos and topo map, I assumed this route would be easy. Difficulties include route-finding challenges, disappearing trail, lots of elevation gain, and a non-trivial ridge traversal with moderate exposure. The route is 14 miles round trip, with plenty of class 3 scrambling on and below the ridge.
Use the Browns Creek Trailhead described on the main page.
County Roads 270 and 272 are in excellent shape, fine for your sedan. There are well maintained restrooms at the trailhead, and plenty of parking. Trailhead elevation is 8900' according to USGS topo map.
The first thing you must do is ignore the dotted red lines on the large wooden sign just beyond the trailhead. The lines are very misleading. Perhaps the trails have been moved since the sign was made.
Follow the main trail 1.1 mile west, to its intersection with the Colorado Trail running north and south. Turn right and follow the Colorado Trail 0.3 miles north to the Little Browns Creek Trail, 1430. Turn west onto 1430. Both trail intersections are signed.
It will be another mile or so before the trail rejoins the creek. Follow the trail several miles up the north side of Little Browns Creek. You may lose the trail in places, but it is there. As usual, the trail is easier to follow on the return trip down. Just stay north of the creek and you will be fine.
Unfortunately, the creek goes underground much of the way, so you can't always hear it. You will only get fleeting glimpses of Mount White during the approach.
At 10,900' or 11,000', cross the creek and head up the east end of White's east ridge. Climb forever up the steep and often loose talus slope until you top the ridge at 13,200. Remember, this is no picnic.
Once you mount the ridge, the difficulties begin in earnest. The first major ridge obstacle is the worst. But you are committed now, so go right over the top of it. There is no way around it. Bypass the second and subsequent obstacles on the ridge by dropping down on the north side.
Halfway across, the ridge becomes smoother and from there it is a picnic.