Just did the run up and over Four Peaks a month ago in the RZR. Ran down to Tonto Basin, had breakfast and headed back. Was a good, smooth trip since the weather was great, slightly windy at the top but nothing too crazy- actually felt good compared to the Valley. Only bad run we've ever had up and over was one January on quads years ago when it was raining/snowing. Needless to say we were not dressed for that and froze, made for a long trip back to the truck.
View from the trailhead on top, looking east toward Roosevelt Lake in the background
As you explore the lower washes near the lake, be careful, as there is usually a lot of traffic and many people are not generally paying attention to what they are doing/where they are going. Some of the closest calls I ever had on the quad & bike have been in that area, several potential head-on's and was once nearly t-boned (ended up laying it down). The brush makes for poor visibility and you can suddenly cross paths without warning. As you may have already seen, there is a bit of everything out there from a vehicle perspective - from the small chinese go-karts to lifted fullsize trucks and everything in between. You never know what you will cross paths with. Also, be mindful of people target shooting. I think they have attempted to curtail most of this in the immediate vicinity of the lake due to the high density of people, but most of the outlying areas in/around Four Peaks road are still open. Either way, keep your head on a swivel.
That said, it is a fun area to run & explore, some of the trails lead to the other side of the 87 (Sycamore Creek / Mesquite wash) if you know your way around the mountains and that can open up a whole new area to explore.
Have you seen this website before? It gives a breakdown of many local AZ trails / areas to check out.