I don't think you'd have a problem with your F150 with V8 and tow package. We pulled our 3124kb over the Sierras and the Colorado Rockies many times without incident with an 06 Tundra with small V8 and tow package.
Hairpin curves depend on the "hairpin." I avoid, for example, the road from Flagstaff to Sedona for that reason. It's a long downhill with sharp hairpins. Hard on brakes as well. There is also a segment of California Highway 49 between Auburn and Placerville I stay off of for the same reason. My rule of thumb is to watch the signs. At least in Utah and California, roads not suited for trailers tend to be marked with large yellow warning signs.
The eastbound grade from Salt Lake City to Park City and then on to Evanston, Wyoming is one very, very long grade but again, with my tow package, I never got overheated and was able to at least stay at 45 mph. That said, I wouldn't want to pull that grade with a mini-van.
With your rig, I think you're suitably equipped to handle your 3326 in mountain driving without problem.
Keith
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