This is so easy. I hike many times over Cottonwood Pass (leaving my car at Cottonwood Trailhead) and exit Cottonwood Lakes trailhead.
Both trailheads are separated by a half mile. There are no ravines, gully's or such to hike to Cottonwood Trailhead from Cottonwood Lakes Trailhead.
So, when you hike out on the Cottonwood Trail, you will come to a junction in the trail, about a quarter of a mile to the trailhead. This junction is the side trail to, equestrian campsites and and finally the pack station.
Take this trail, it passes to the right of the equestrian campsites, then passes to the right of packers station. There will be horse arenas (filled with horses and mules) to your left (you're still on the trail), when you get to the end of the horse corrals, the trail heads west and meets up with the Cottonwood Trail, right at the junction of Trail Pass junction.
At this point, walk down the gentle slope (oh so easy, through the trees), angling to your left as of the you hike down, about a quarter mile, you, depending how much you angle left, you will either intersect with the Cottonwood trail, or parking lot where you left your car.
paul