White Mountain is not all that dramatic, and is frequently overlooked due to its proximity to Mt. Conness and Ragged Peak, both of which are more visually interesting. The Secor guide states that it was first climbed in 1917 by Walter L. Huber.
While the summit may not be particularly noteworthy, the hike to and from White Mountain can be leisurely and highly enjoyable; I wouldn't hesitate to recommend it for someone's first Sierra peak. The south slope is class 2, and it only rises a little bit above 12,000', so it is reasonable for the beginner.
White Mountain is frequently confused with "False White Mountain", which lies just to its southeast. See the links for a ski tour from False White.
There are several routes to get to the summit of White Mountain, three of which are inside Yosemite, and one of which (the eastern approach) comes in from the Hoover Natural Area near Saddlebag Lake. The easiest approach would be to park at the Dog Lake trailhead in Tuolumne Meadows. Follow the trail past Dog Lake and towards Young Lake.
About a mile in, you will cross Delaney Creek. Leave the trail here and walk east through the two gorgeous meadow systems along the creek (they are separated by a patch of forest). You will re-enter forest after the second meadow, and then come out near treeline. The southwestern slabs of White Mountain will be directly in front of you on the left; this route is class 4 and involves some loose, sandy scrambling above big drops. If you want to keep it mellow, continue straight until you hit Skelton Lakes, then follow the easy south slope to the summit.
The summit can alternately be reached from the Young Lakes basin by gaining a notch in the ridge between Conness and White, then following the ridge south. The eastern route, which leaves from near Saddlebag Lake, is at least class 3 and might involve snowy conditions. I looked down over the ridge towards Saddlebag in July of 2002 and there was a snowfield for about as far as I could see.
There is a $20 fee to enter Yosemite National Park.
There are no fees for day hiking, but if you are camping overnight you will need to obtain a wilderness permit (free if you get it the day of your hike).
If you are backpacking, please spend $5 on a bear canister rental and keep your food away from Yosemite's bears.
There is no parking pass required at the trailhead, but you would be advisied to remove ALL smelly items from your car and put them in the complementary bear lockers. There is nothing enjoyable about coming back from a peak-bagging trip to find that you now have a 3-door sedan.
When To Climb
The south slope of White Mountain should be free of snow by July, depending on the year. I have read accounts of enjoyable ski tours from its summit, as well, but I can't speak for them personally. See links for a description.
See comments above regarding backcountry permits in Yosemite. Camping is allowed in the Young Lakes basin. Camping is not allowed in the area that extends between the Ragged->White crest and Highway 120. This includes the Delaney Creek drainage.
I can't speak for camping in the Hoover Natural Area, although there are several cheap primitive campgrounds along the Saddlebag Lake road.
The Tuolumne Meadows wilderness permit office will have up-to-date information about backcountry conditions for the Yosemite high country, but don't waste your time calling them before the second week of June or after the first week of October.
Thanks to fedak for the following information.
From Peter Browning's Yosemite Place Names:
White Mountain was probably named by the USGS during the 1898-99 survey for the Mt. Lyell '30 map.