The winds you saw hit a lot of the West pretty hard. That said I've been through both States a few times and you really need to pay attention to the weather reports for the area you are driving. We live in WA State and the Columbia River Gorge between OR & WA gets a lot of winds. My wife checks each of the areas along the route so we know what we're driving into.
We saw truckers and RV's taking the exits to park in under passes or rest stops when the winds picked up. Just be smart and know before you go.
I do agree with Dave, 15 is a better route IMHO. You might take 40 then grab 89 out of Flagstaff and to Kanab then 389 to 59 to 15. We drove that last section to Kanab and it was pretty good road the whole way.