I've just returned from an enjoyable event in Rustigazzo, Italy. Often I wonder how women of the epoch coped with travelling in hot climates without getting burnt and keeping cool. Of-course I had the advantage of getting refreshments and wearing sun tan lotion but wearing a veil with your hat makes sense. Combined with a parasol, long gloves and a good fichu or chemisette you can get a lot of protection from the sun.
I've found many good 19th century veils on ebay and antique markets for under £20!!