In our report, we have sequenced Mt. Ridgway with Whitehouse. Since they both largely use the same route for much of the way, you might as well do these two together, especially considering the bushwhacking effort you'll put in.
From the "upper" trailhead, hike NW up a hillside on the "Dallas" Trail #200 and contour around the nose of a tree-covered ridge. You'll then be heading SSW and will cross a minor creek drainage which is actually the west fork of Coal Creek you drove/hiked across earlier to reach the upper TH. After crossing, the trail turns NW again, rounds a broader ridge and turns SW and joins an old roadbed for a short distance. The trail then crosses Beaver Creek, heads up a small ridge, then crosses a minor tributary to Beaver Creek. Less than a half mile after crossing Beaver Creek, watch for the trail to head south and follow an old roadbed uphill. On the Trails Illustrated map #141, this is the Wilson Creek Trail #202 which will lead you up to the Ridgway Hut at 10,200 ft. On the Uncompahgre NF map, this remains trail #200. The main point is to get yourself to the Ridgway Hut at these coordinates: N 38° 02' 24.81" W 107° 46" 05.81". When we hiked this last section in 1998, we found an old roadbed that switch-backed multiple times as it led uphill to the hut. It's possible the trail along this section has now been revised because more recent maps do not show all the switchbacks. The climbing route will start from the hut.
If you've made it to the Ridgway Hut, head SE from the hut, initially through some open forest and then into dense trees with enough fallen timber to look like a giant game of pick-up-sticks. It will look almost impossible to navigate but there are numerous game trails (elk mostly) that penetrate the fallen log maze and lead you to a ridge on the west side of Beaver Creek. Follow the ridge SSE utilizing the game trails as best you can. In about 3/4 mile, you'll need to drop a little and cross two open avalanche chutes a little below the 11,000 foot level. Any trail you may have been following will disappear here as dense vegetation obscures it and hidden obstacles like boulders and logs.
After tripping your way across the avalanche chutes, continue contouring SSE toward Beaver Creek and hopefully come out near where two minor drainages join in with the main flow at 11,000 ft. If you're alert, you may be able to find a clear game trail that will take you through this last section over to Beaver Creek. Head now for the main saddle between Whitehouse and Ridgway. Hike up a steep ridge between two stream courses that's mostly tundra with a few trees. If you're lucky and quiet, you may see some elk here. The open ridge is crisscrossed with their trails and you'll see areas they have leveled out for sleeping and ruminating. Continue up this ridge until it plays out.
Head on into the main gully that leads to the saddle. For the next 1,000 feet, the going will be mostly on loose rock and sandy gravel. A game trail continues up through here that both elk and bighorn use to access Weehawken Basin. The last few hundred feet will be quite loose but not too difficult with the aid of the game trail. From the saddle, head up another minor couloir that leads upward to the east (left). The rock-filled and loose gully provides a break in the cliffs that surround Whitehouse. After about 200 feet of ascending, the couloir will play out. Continue ascending on small, loose rock until you break out onto the flat, summit area. Stroll the remaining 3/4 mile over to the true, eastern summit. The broad, flat summit expanse is large enough to host a football game. On either side, there are amazing views of the surrounding, rugged mountains.
For your return, we suggest going back as you came. If doing Ridgway as well, hike back down to the Whitehouse/Ridgway saddle to begin that ascent. Also, it may be possible to hike over to Corbett, but there will be a significant drop off the summit of Whitehouse to negotiate. Sorry - we have no beta on attempting that traverse, but a few photos may help.
Links to other information, routes & trip reports for this peak that may be helpful.