Does wearing hats make it harder for others to shoot you?

I use the Master's yellow belt (painted black, of course) or other small hats.

The other larger hats may throw off some noob snipers, but I prefer to minimize my visual profile to avoid being seen as much as possible. Sometimes large hats can be seen over a fence or other obstruction when the sniper would normally remain unseen. The snipers nest area in hightower, for instance, has a fence leading up to the stairs that would allow a large hat to be visible behind.

Sniper battles are ideally won by attacking from an unexpected direction.

Ritzy Rick's Hair Fixative? (aka no hat)

Towering Pillar of Hats is obviously very conspicuous, but maybe people will try shooting the top of the hat and miss?

In reality it's going to make very, very little difference.