The best way to approach C.T. Peak is either via trail along Cooper Creek or via the ridge hike combining it with other 13ers.
One can start near the summit of Cinnamon Pass (or at its summit) - part the scenic alpine loop connecting Silverton and Lake City. This road is a rough 4WD road and very popular with ATVs.
Or you can start hiking Cooper Creek Trail - signed trailhead below Cinnamon Pass.
How to reach Cooper Creek Trailhead: From Lake City, drive south on 149 and take the turnoff the right for Lake Cristobal. Continue south along the lake and follow the scenic alpine road past the Williams Creek and Mill Creek campgrounds to the intersection for Sherman (winter closure past this area). Take the right fork on start an ascent towards Cinnamon Pass. This section of the road is exposed shelf road. After about 3 miles you pass popular trailhead for the Silver Creek/Grizzly Gulch (access for 14ers: Handies, Redcloud and Sunshine). Continue one more mile to a small parking lot and trailhead sign for Cooper Creek.
Ridge between C.T. and Gudy Peak
As any mountain there are many options to reach its summit.
I came from UN 13427, then UN 13540A with a start below Cinnamon Pass - the descent from UN 13540 was steep, exposed and rocky. I stayed on the rugged ridge of UN 13540, but there was an easier option to drop below the cliffs on its southern side. I would recommend to bypass the ridge proper since I ended up with some loose 4th and short section of 5th class scrambles. There is a large grassy saddle between UN 13540 and C.T. Peak and the then mostly grassy slopes up the ridge of C.T. Peak leading to its summit. The main summit cairn (highest point) is located at the northern end. The summit has great views with 5 nearby 14ers: Wetterhorn and Uncompahgre, Redcloud and Sunshine, and finally Handies Peak.
From the summit I continued towards Gudy Peak. The descent from C.T. Peak involved a steep ridge (class 2+) to the saddle of C.T. Peak and Gudy Peak.
Another option would be to hike up Cooper Creek Trail and combine Gudy Peak with C.T. Peak (shorter version), or add "Every Mountain" and "Cooper Creek Peak" (long day).
The east facing slopes leading from the Cooper Creek Trail to the saddle between Gudy Peak and C.T. Peak are mostly steep grass. I came down this way.
There is no red tape. Driving the Colorado Scenic Highway, parking and hiking are free.
When to Climb
Summer is obviously the easiest time to climb with a nice access and safety. Winter adds at least 4 more miles each way to approach Cooper Creek TH and danger of avalanches. Always check avalanche conditions prior venturing out during the winter.
Late spring and early fall may offer good opportunity for exploring this peak.
There are designated campgrounds at Williams Creek and Mill Creek campgrounds. You can find free primitive camping at the trailhead and also at the trailhead at Grizzly Gulch.