Here are some shots from up there on May 6, 2013 during one of my epic ski trips last spring.
Any non-motorized route (as per current landowner's request) is a good route. The most conventional route up Mt. Houghton is the old trail up the easiest West facing grade. You can drive all the way up to where this trail begins. It's now a little hard to find. There was a gate there and a copper sign (in cooperation with the Keweenaw ATV club) requesting no motorized travel beyond that point. But the gate was ignored, and within a few months the sign was stolen, so the landowners took more draconian measures and eliminated the first few hundred yards of the trail, but you can still find it a little ways up past the location of the old gate. I go up there almost every week or two so I know well the trespassing that continues on occasion, although most people respect the wishes of the landowners. If anyone claims to have permission to ride a motorized vehicle up there, please let me know and I will clarify that with the landowners.