When hiking Picketpost on the normal route from the trailhead just off the US 60 you get a 1.5 mile warm-up before the 1 mile climb to the plateau. Not from the east... The drive to the TH will be challenging enough for most hikers then you barely have a 100 yard warm-up before beginning the roughly 0.9 mile climb to the northeast corner of the plateau. Your route will vary and very likely you will seek an easier route on the return so your route selection skills will be put to the test. While I did not successfully make the summit on my first attempt, I know the route is doable. I was within 300' of altitude of the horseshoe cross when I had to turn back due to weather fast-closing to the point I could not see 20' ahead. Another attempt is coming very soon, when I will also try a completely different (and steeper) return route.
Picketpost from the west is something any hiker in decent shape can do... Picketpost from the east? Well this one will separate the men/women from the boys/girls. You'll need good climbing skills (no ropes!) and plenty of stamina along with a willingness to travel up steep and at many times loose terrain that may slide with no prior warning. But for those who consider themselves worthy of a challenge (albeit a short one) it's a great way to see and experience awesome views from a completely new vantage point.
If you enjoyed the 4x4 drive to this trailhead, I'd recommend you continue on FR 4 all the way across to the east past Ajax Mine and out on SR 79 about 5 miles south of Florence Junction. (If you take this route you will need an Arizona Land Trust Access permit)
Check out the Official Route and Triplogs.
This is a more difficult hike. It would be unwise to attempt this without prior experience hiking.