The part of this that caught my eye was the indication that you are thinking about putting in a, "lining."
To be honest, by the time you put a vest and coat over this shirt you would typically be heading out of a comfort zone, if it will be used in moderate to warm weather.
However, if you are actually thinking about making a shirt for very cold weather, cotton should probably not be your first choice of fabrics in the first place.
A white pleated front and collar would likely be the only part of the shirt showing if worn under a vest and coat. In other words, the shirt would probably look like a white shirt based on what would show.
Pleated white shirts were typically not worn as work shirts. If he will be working and will only have a vest on over the white pleating, with the other fabric showing, it will look odd in my opinion.