Same thing happened to me and my 2014 F-150 XLT.
Outside temp was around 10F. I was driving about 35mph and all of a sudden this loud noise started. It literally shook the whole cab.
I figured out it was something to do with the blower. I did the confirmation by turning the fan speed all the way down to low and the loud noise/vibration went away. When I turned the fan speed up it came back again.
I left the fan speed on low (lowest or next lowest setting) and that worked until I had time to research the issue.
Thanks to everyone on this thread. The info was a great help!