The first requirement of this climb is that it must be done in the snow. In fact, be sure that there's at least
a foot of snow covering your route, because otherwise you're climbing the mountain illegally!
The north ridge route is almost always the best way to the top of Agassiz. Follow signs to the Arizona Snowbowl, which is north of Flagstaff on route 180 (the road that goes to the Grand Canyon). Park at Snowbowl and take the Humphreys Peak trail exactly as though you were going to climb Humphreys Peak.
The trail switchbacks through the forest on Humphreys' west face and finally gets above treeline and leads to a saddle between Humphreys and Agassiz, at about 11,780 or so. From here the trail continues north to Humphreys. To climb Agassiz, leave the trail at this point and simply follow the ridgeline south toward the peak.
Be careful not to get on the Weatherford trail - this heads south but will lead across the east face of Agassiz and finally drop you into a saddle between Agassiz and Fremont. What you want to do is just follow the Humphreys-Agassiz ridge to the summit of Agassiz. The summit is slightly less than a mile from where you get off the Humphreys peak trail. It's about 600 vertical feet up as well.
From the summit you've got at least two good options for getting down. Probably the simplest is retracing your steps. A second and faster way is - conditions permitting - to head down the ski slopes west of Agassiz. If you've brought skiis this is even faster, but glissading down is an option as well.
Gear depends on the conditions, but gaiters, warm clothes, and good boots are a necessity. Sometimes snowshoes are helpful if the snow on the Humphreys peak trail is heavy. Although the route as described is not technical, an ice axe and knowledge of its use is recommended.
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