During periods of lower humidity, cooling tower plumes are less prominent meaning that they contain less visible moisture. It is this "visible moisture" - meaning that the plume contains more droplet sizes that can be seen with the naked eye - that is falling out and leaving the salt and minerals and chemicals behind that the OP mentions.
On a dry day, the cooling tower is more efficient and less moisture leaves in the airstream as visible droplets - with, of course the better performance and wet bulb temp. The same amount of moisture leaves the tower however, - thermodynamics dictates that, just less as visible plume.
I live in a climate where it is humid to some extent most of the times, but on those hot summer afternoons when it is dryer you really have to look closely at some CT's to see if their units are on line, and you know that they are that time of day. Driving by the same tower in the humid early morning hours, and it is like two different towers.
A perfect cooling tower would be one that evaporated the water needed to cool water adequately without having any carryover. Since that is easier to do on dryer days, there is less carryover. On humid days, every tower struggles.
rmw