Hidden Peak is home to the Snowbird Tram, thus, it is probably the most frequently visited peak in the state. While some might scoff at this destruction of the mountain's natural state, it does offer people who maybe could never get there on their own a chance to view one of the best views around.
Hidden Peak was the first legitimate mountain I ever climbed. In 1984 I hiked up Gad Valley to the peak with my dad and my brother Steve. It was hard and tiring, but I loved actually climbing the mountain rather than just taking a tram up. Obviously that trip started a favorite hobby of mine. I've since climbed the peak seven more times, plus countless tram rides. The most common routes are Peruvian Gulch from Snowbird, and Gad Valley from Snowbird, but my favorite way to the peak now is to get a ride to Albion Basin at Alta. Hike past Secret Lake, up and over Mount Baldy, then to Hidden Peak, and hike back down to Snowbird.
The most common route however up the peak is Peruvian Gulch. It is nothing more than a wide ski patrol road. Consult Snowbird hiking guides for the trails to take as they change constantly, particularly in Gad Valley. The Peruvian trail is about 3.5 miles, gaining 2,900 feet. Reaching the summit takes about two hours from this trail. Along the way you'll have good views back across the canyon to Mount Superior. In late 1998 I took the tram up, crossed the ridge to Mount Baldy, and hiked back down with the upper part in complete snow.
The Gad Valley trail is about four miles, climbing 3,100 feet, so add about 15-30 minutes hiking time to this route. Both hikes start typically at the Snowbird Center, but the Gad Valley route quickly heads west and winds up that canyon. It passes under the massive American Fork Twin Peaks, and tucked away in there is a "rock glacier", but it is often snow-covered. The final switchback is a favorite of mine, offering a great view back down the canyon. This canyon has a more "natural" feel than Peruvian Gulch does, but even that is diminishing as the years go by.
In past years, they've given hikers free rides down from the summit should you desire to go down that way. More recently they've advertised the tram as pay for each direction, but I've never seen them stop anyone on the trip down and make them buy a ticket. As mentioned, the view is superb. The summit offers great views of most of the highest, most prominent Wasatch peaks. A short hike across the ridge towards Baldy will give you a view of Timpanogos (blocked by American Fork Twins on Hidden Peak). Check the Mount Baldy link for better pictures from the area. Clockwise from the bottom of Little Cottonwood Canyon you'll see Broads Fork Twins, with Sunrise and Dromedary Peaks nearby, the rugged Cottonwood ridge leading to Mount Superior which is directly across the canyon from Hidden Peak. Flagstaff Mountain and the peaks of the Brighton area are not as rugged and obvious as the others. Nearest is Mount Baldy, but you'll also see Sugarloaf Peak and Devil's Castle in the distance. Mineral Basin below is now part of their ski resort. Far in the distance is the double-peaked Provo Peak. Huge American Fork Twin Peaks usually retains some snow patches year-round. Behind that lurks the sharp Pfeifferhorn, and even further out you can barely make out the tops of Lone Peak and the Thunder Mountain ridge before it dips back into Little Cottonwood Canyon.
If you decide to hike down, the most difficult part will be not getting onto wrong turns on the roads down both canyons. If you finish and desire a good meal you might want to check out the Steak Pit, arguably the best steaks in Utah, and my favorite restaurant!
2002 Update: Made my 9th ascent of Hidden Peak (most of any peak I've done) on October 19th via Peruvian Gulch. I started just after 9am, and had a little trouble finding the way to the obvious road under Mt. Baldy. Best bet appears to be to park near the parking structure for the Cliff Lodge and find the small trail leading up a few hundred feet to the main service road. From here it is easy to follow (despite a few intersections) to the summit. It was a cold day as one would expect in mid-October, and the upper half of the mountain was retaining a good deal of snow from a storm two weeks earlier. The upper part was well-beaten and very packed (downright icy in spots). As usual, the summit was laden with tourists from the tram, but the views were typically outstanding. The trip down was tricky on the well-packed snow and I took a slip in one spot landing on my behind. Once out of the snow, a routine descent. One note of interest is that Snowbird has constructed a new route to the summit of Hidden Peak via the north (main) ridge. Hike up Peruvian about half way and you'll see the obvious switchback leading up to this ridge which is almost directly under the path of the tram. A hiker I ran into says it was constructed new in 2002 and the trail is followable right to the summit, no scrambling. I'll add this to the "to do" list for next year hopefully!