Tibble Fork Reservoir Trailhead
From Interstate 15 take Exit 294, Highland Alpine, Route 92 east towards American Fork Canyon. At the mouth of the Canyon you will come to the intersection with Route 146. From this intersection continue straight on Route 92 for 5 miles until the road splits (.6 miles past mile marker 12). Take the left fork, Route 144 for 2.1 miles to Tibble Fork Reservoir where you should park. If the lot is full, you can continue .3 miles to a much bigger parking lot, with an outhouse. In the winter, this is where the plowing ends.
Mill Canyon Trailhead
From Interstate 15 take Exit 294, Highland Alpine, Route 92 east towards American Fork Canyon. At the mouth of the Canyon you will come to the intersection with Route 146. From this intersection continue straight on Route 92 for 5 miles until the road splits (.6 miles past mile marker 12). Take the left fork, Route 144 for 2.4 miles to the end of the pavement. In the winter you will have to park here. Continue straight for .15 miles on a dirt road. There doesn't seem to be any official place to park. I just parked at the side of the road. The trail goes down hill a very short distance to meet American Fork Creek and continues on the other side. The creek is shallow but wide. There is no bridge and even in the middle of winter was not frozen over. Therefore, unless you don't mind getting your feet wet or come prepared with appropriate foot wear, I don't recommend starting here.
As far as I know, this route is the easiest way to climb Mill Canyon Peak in the winter. Starting from Tibble Fork Reservoir, round trip, it is 11.5 miles with a 4200' elevation gain. In the winter, it took me 4:40 to get to the summit and 7:45 round trip.
The short version is, start at the reservoir, cross the bridge, walk along the SE bank of the reservoir, ascend Mill Canyon to Mill Canyon Peak's SW ridge, follow the ridge to the summit.
The long version:
If you don't mind getting your feet wet (see the Getting There section) you can start at the Mill Canyon Trailhead. If this is a problem for you, park at the Tibble Fork Reservoir Trailhead and walk across the bridge. At the far side of the bridge, just after the bridge, on your left, you will see a fence with a gap in it. Go through the gap and walk along the SE bank of the reservoir and creek until you reach the trail sign for the Mill Canyon Trail (#040) at N40 29.017 W111 38.411 in .45 miles from the start. I did this in the winter on snowshoes when all of the brush was covered and found a well trod, easy to follow path. I don't know what this would be like in summer, but I suspect there is probably a trail. But, in summer, it would not be unreasonable to wade across the creek near the actual trailhead. One caveat for the winter, is that the path around the reservoir is right next to the water in a few spots, slopes toward the water, gets a lot of sun, and if it hasn't snowed for a while could be very interesting first thing in the morning before it softens up.
Follow the Mill Canyon Trail (#040) for .9 miles to an intersection at N40 28.653 W111 37.695 with trail 173 which leaves to the right. Stay on 040 for another .9 miles to an intersection at N40 28.583 W111 36.712 with trail 039 which leaves to the left. In another .75 miles I came to an obvious fork. The trail went to the left, but the snowshoe track went to the right up a gully to the Ridge Trail (#157). This fork may not be apparent in the summer or with fresh snow. You want to bear left and stay on the trail for another .75 miles to a big intersection at N40 28.44 W111 35.274 with the Corral route and the Tibble Fork route.
In the summer, take the Ridge Trail (#157) in a generally NE direction until about 9240 feet near the beginning of a long traverse across Mill Canyon Peak's western slopes. Route find across a sage brushy slope about .1 miles east to the top of a ridge. Follow the ridge generally north to the summit about .7 miles.
In the winter, once you get to the big intersection with the other routes, the trail will no longer be apparent and you can just follow the ridge to the summit. In the vicinity of this intersection you will probably encounter a few snowmobile tracks. I've never actually seen a snowmobile though and I've found their tracks a welcome relief from trailbreaking.
This is the quickest route to the summit that I know of (if your car can make it to the corral) but the trailhead is only accessible in summer months. From the corral (see the "Getting There" section) proceed NNW up a rutted trail about .5 miles to a big intersection. Take the Ridge Trail (#157) in a generally NE direction about 1.2 miles until about 9240 feet near the beginning of a long traverse across Mill Canyon Peak's western slopes. Route find across a sage brushy slope about .1 miles east to the top of a ridge. Follow the ridge generally north to the summit about .7 miles.
Starting from the corral, the total one way mileage is 2.5 miles and the elevation gain is 2400 feet.
This route is a long way, 20 miles round trip with round trip elevation gain of 6000 feet. Most of the way you are on the Great Western Trail (GWT) which runs from Canada to Mexico passing through Montana, Idaho, Wyoming, Utah, and Arizona. The GWT is a multi-use trail and the section from the top of Dry Fork to the base of Mill Canyon Peak is open to off-road motorcycle use.
Start at the Catherine Pass Trailhead. Head towards Catherine Pass which you will reach in about 1.5 miles. At the pass, you will intersect the GWT. Follow the GWT 2.3 miles up about 300 vertical feet and then south down Dry Fork to about the 8800' level. You will loose 1640 feet of elevation (a big drag on the way back). Continue on the GWT .4 miles east to the ridge running between Sunset and Mill Canyon Peak. Continue on the GWT another 5.2 miles, sometimes on the ridge and sometimes contouring next to it until about N40 30.106 W111 35.106 where the trail is about to go around knob 9620. Leave the trail and head up a gully to a ridge that runs east to join the main Mill Canyon Peak Ridge. Once on the main ridge, head south to the summit. This off-trail section is about .7 miles.
An alternative to dropping down Dry Fork would be to ascend Sunset Peak and follow the ridge SSE to the 9400' saddle where you will meet the GWT. I do not recommend this way because there is a nasty stretch right in the middle. It will start out mellow and end mellow, but the crest of the ridge in the middle is very blocky. I stayed on the SW side and traversed just below the crest across a steep slope consisting of a thin layer of pea sized gravel on slick rock. Taking this variation turns an easy but long class 1 hike into a minimum of class 3.