Pretty sure its the power steering pump. I had a continuous whining sound and replaced the fluid with LucasOil Power Steering Fluid. This took out the continuous whine but I now have had the exact same sound on startup, and only in the cold. Truck was 9 years old when this began.

 

I've owned the truck since new. It's done it since the first winter I had it, with probably 5000 miles. 103k now, only happens on extremely cold days and doesn't worry me.

 

Just saw this post. Mine sounds exactly the same and has since new on first start after sitting with temps below zero.