This is a nice way to get all up on that summit of Mt. Hood. It would seem the prime time would be late winter or spring. We were able to find some nice ice as late as June (in 2013), but we were racing the sun. Rockfall becomes an issue with warmer temps as the crumbly headwall showers down on your head like rocks often do. Depending on the time of year, you'll encounter alpine ice to plastered snow in different forms in the rocky runnels. In mid-June we found good ice (but melting fast) - earlier in the season would most likely yield safer conditions. I may also be talking out of the ole behind on this one - have only been on Hood once, and was surprised there was no route page for this, so I MADE ONE.
You can cross the lower glacier from the point described above, heading west/southwest over a few sections of moraine to the western side of the Elliot glacier. You'll ultimately head south up a huge slog up to the top of Snow Dome orrrrrrrrrr you could just climb up the glacier proper to the base of the headwall. The choice is yours - the slog up SD is less technical and most likely faster. From the top of Snow Dome, head either directly left through the icefall to the base, or you can cross the big crevasse just below the clump of rock, and head up and around the small clump of rock's right side before you traverse over to the base of the headwall.
There are several crevasses to deal with (hopefully with bridges). The headwall itself is a choose-your-own adventure kind of thing, look for where the lines go and GO. Depending on how direct you are able to climb, the number of pitches will vary. We headed far left from Snow Dome to cross at the easiest spot, and then had to traverse to the right side of the wall, head up, then traverse far left due to rockfall lines. Depending on your skill level, you can simul or pitch it out. The climbing is fun and moderate, with a few short steps in the ice depending on conditions.
You can emerge pretty much on the summit, depending on the cornice situation, etc. We traverse far left, joining what I think is the North Face routes for a nice arete of Neve to the top. Again, once you're below the wall, you can see where to go. It ain't rocket science. Descend the Sunshine or back down the southside if you've got nice friends that will pick you up.
There are several options I'm told - a certain Ukrainian gentleman told me you can do the regular route from the south side and drop down over to do just the headwall.
If you want to be a man about it, you can start from the north side and earn those swings. Depending on the time of the year, access to the roads on the north side may be restricted. We had hoped to start at around 5900 feet or so near the Cloud Cap Inn, but there is a gate (that was locked) at a trailhead at about 3800 feet. Starting from this lower point will take you up and past the Tilly Jane cabin to join the trail heading up the Cooper Spur. The trail from the Cloud Cap Inn also joins this route, and you'll drop down towards the Elliot Glacier from the beginning of the spur route at the large cairn marking a use trail. This is the same approach you'd make for the Sunshine route or the Elliot Glacier from the trailheads.
Two tools (or short axe and a tool), 5-8 screws, couple pickets.