Note: The following route description is provided by Shaun Cooney who climbed this summit in late August, 2016. Additional editing provided by Tim & Carrie Cooney.
If driving a 2WD or other vehicle that you highly value, it's best to park at the place where CR 12 makes an abrupt left turn to cross Mosquito Creek. The route for Tweto and Arkansas continues straight to the NNW, on what is labelled as FR856 on the map we present, instead of making that left turn. High clearance 4x4 vehicles can continue NNW on up a 4x4 track marked on various maps as either FR856 or FR783. This road is very rocky, very primitive, and definitely rough in places; recommended mainly for ardent 4-wheeling enthusiasts or those determined to shave off a few extra miles while possessing a generally cavalier attitude about the condition of their vehicle. The lower section is tightly wedged in between willows, so your turnaround options are limited until it begins switchbacking up the hill. We found one minor pull-off about 1/4 mile up the road that we elected to park at and began the hike from there.
NOTE: The lower section of this road is quite rocky and your options to avoid the larger rocks are often limited due to the encroaching willows. While it wouldn't necessarily require a modified vehicle to navigate this road, it would make the trip more pleasant. Once you reach the switchbacks, the road begins to show more of a dirt/rock mix. A few of the switchbacks are moderately loose and lighter trucks/SUVs may have issues getting enough traction if not weighted. Once above the switchbacks, the road turns into a more of a double-track with the tundra slowly attempting to reclaim portions of it. This is not a popular or well-driven road.
If you elected to park as suggested, hike up to the first switchback where a short spur road branches off. From here you have two choices. Your goal is to reach a saddle at 13,250' to the southwest of Mt. Tweto that connects with Treasurevault Mountain. To get there, you can either follow the road as it switchbacks and turns to the east/right (adding extra mileage), or you can take a more direct approach up the basin. The lower portion of the basin has quite a few willows and will likely be marshy in early summer or after sustained rains, but those obstacles can generally be avoided if a little care is taken. Choose your route and proceed up the basin, veering toward the west once the terrain below Treasurevault's E/NE slopes allows you to do so. As you approach the saddle, the terrain becomes a bit more rocky. From the saddle, proceed up the ridge to the summit on interminably rocky terrain. To return to the trailhead simply retrace your route back to the car. Avoid any temptation to drop directly off the south slopes of Tweto into the basin. It will likely not be worth the short distance you'd save!
Mt. Tweto also combines well with Mt. Arkansas' SE Ridge route and/or a ridge traverse over to Mt. Buckskin. If combining with Mt. Arkansas, it's possible to skirt the summit of Mt. Tweto on either your ascent or descent by traversing across west slopes of Tweto at the level of the Mt. Arkansas/Mt. Tweto saddle. This slope is a little looser & rockier than the ridge, but is just stable enough to make the traverse at least a minor time-saver.
Tweto may also be climbed from the south via Mosquito Pass, Kuss Peak, Mosquito Peak and Treasurevault Mtn. See Treasurevault for more detail.