The first recorded climb of Snow Mountain was in 1915 – it was then called Mt Silvia, and is now also spelled Syueshan, Shueshan and Xueshan. Since then this sublime peak (Taiwan's second highest at 3886m) has attracted teams and solo hikers from all over the world.
The trail, from the ranger station trailhead in Wuling to the summit, is 10.9km and takes 9½ to 11½ hours to complete (one-way). Because of the altitude gain, and the fact that most people are carrying heavy packs, this usually requires two days (with a third for the return):
Trailhead to Chika Cabin 2km, 1½ hours
Chika Cabin to 369 Cabin 5.1km, five to six hours
369 Cabin to Main Peak 3.8km, three to four hours
The trail to the main peak is for the most part broad and clear, and requires mere fitness rather than any technical skill (unless you're going in winter). The first day's itinerary is always a bit tricky. If you have taken a bus and walked (or hitch-hiked) the 7.5km to the trailhead (2140m), then you aren't likely to get any further than Chika Cabin the first night. Nor should you, as it's best to acclimatise at this elevation before going further.
The second day's hike is a long series of tough switchbacks (one is even called the Crying Slope). But the views on a clear day are stunning, and the landscape is ever-changing: from forested cover to open meadowland, to fields of Yushan cane. The box-fold cliff faces of the Holy Ridge are unforgettable.
At 369 Cabin, a sturdy shelter nestled on a slope of Yushan cane, most hikers overnight, getting up at 2am so that they can reach the summit by daybreak. Unless you know the path to the top, it's really not advisable to do this.
So, assuming you get a reasonable start you'll soon be in the Black Forest, a moody stand of Taiwan fir. At the edge of the forest be on the lookout for troops of Formosan macaques. Note that the giant hollow before you is a glacial cirque formed by retreating ice fields.
It's another 1km from here to the summit along more switchbacks. Unlike Yushan, the summit of Snow is rounded and requires no climbing to mount. But you'll want to linger here and take in the Holy Ridge and other surrounding peaks.
Hikers normally reach the summit of Snow and then return to the trailhead (and their vehicles) on the same day. You need to leave 369 Cabin no later than 6am to accomplish this before dark. For reference: from the Main Peak back to the trailhead takes about six hours (two hours back to 369 Cabin and a further four hours from there to the trailhead).