I too have been having this issue, I bought my truck new in may of 2016 and about 7 months later, I started to notice a whining noise during cold starts on colder mornings. Now its louder and it does it just about every time I start it. I've took it to the dealership, but of course they can't duplicate it. Has anyone found a solution yet? It does sound like something to do with the power steering.
Since no one else has posted a video yet, I'll try to get one posted in the next day or two.