Big Horn is a sharp pinnacle of crumbling volcanic rock, highest in a set of rugged crags to the west of Mount Gilbert in the Goat Rocks. Gilbert, highest point in the area, is a relatively easy ascent, and normally only a few seriously masochistic hard-core climbers would venture out to a summit like Big Horn. But Gilbert sits east of the Cascade Crest that forms county lines in Washington, leaving this imposing crag the highest point in Lewis County. So a good portion of the interest in the unofficially named Big Horn is from peakbaggers after county high points.
This is a serious mountaineering objective. Before attempting Big Horn, you should have: experience with steep, very loose Class-3 rock; someone who can lead a short mid-fifth class crack; ability of all party members to climb that with a top-rope; comfort with very steep snowfields (unless you go in very late season, maybe); a small party size (4 or less) due to extreme rockfall danger; and the following gear: helmet, rope, harness, a few small cams or nuts, slings, ice axe, crampons.
No one who has ever done Big Horn wants to do it again. The short rock-climbing pitch gives this peak its notoriety, but Bob Packard is correct when he says the hundreds of vertical feet of terrible loose rock and/or steep snow are the real challenge. This peak definitely deserves its "Apex" rating as one of the toughest 20 county high points in the 48 states.