The decision to have a veil nowadays rests entirely upon a bride's choice, of whether to stay strictly with tradition and go the whole hog till the very last second, or abandon the whole thing based on the style of her wedding dress or theme to the wedding.
Some brides will feel that as this is the only time she will ever have a legitimate excuse to wear a veil, she must have one, just to say "I did".
The tradition of the bridal veil descends from two sources. Firstly, the veil was an outward sign that a woman was spoken for and all others should keep clear. Secondly, it was deemed as a disguise so a woman would not be recognised by evil spirits wishing to harm a vunerable bridal couple. Some say that the older the veil the better and if borrowed from a happily married woman, that luck will pass on to the new bride wearing it.
By tradition, the bridal veil should be left off till the very last minute before a bride leaves for the ceremony. Plus, the bride should not look at herself in the mirror once the veil is on, with it not being raised till she meets her future husband at the altar.
Quirky as these traditional meanings are, it's way, way out of date by most modern brides' standards. Most brides will make a choice on the wearing of a veil in keeping with the style of headdress worn, taking into account the design of the back of her wedding dress and whether the gown has a train or not.
So, it falls down to this - wearing a bridal veil on your wedding day, is just a matter of choice.