I’ve hiked it extensively except for the southwest portion. Barnhardt trail is an absolute must, one of the top 5 classic hikes in Arizona (outside GCNP). I’d park at the Barnhardt trailhead and then hike 7 miles up to the Mazatzal Divide trail (also AZT). Head north from there.
I can’t tell exactly what trails you have planned out but I have a very detailed USDA Forest Service map of the Mazatzals I’m looking at. Appears as if you’re wanting to go up just west of Pine and then over to the Verde River Trail and south. That would all be doable, however from Horsehoe Lake east I’d be ready for some extremely rugged terrain and hard to follow trails.. Don’t want to dissuade you because I love the Mazatzals, it’s kind an underrated gem in my book. But it ain’t no game and I’d certainly have my water situation planned out. Hardcopy maps as well as GPS.
Water is scarce, mostly seeps at best, so you probably want to do some water drops. And if you get into a stretch where wildfires have gone through, it can be 1 mile per hour. Scenery is all worth it though and you won’t come across many people. Highly recommend.