When I first read this, I assumed this practice was widespread, and used to combat some silly superstition, either that it brought good luck to the wearer or bad luck to the other team. After some quick research, I discovered I was quite wrong! It seems this rule was instituted because of just one player. Claiming to be sensitive to heat, he began putting a frozen cabbage leaf under his cap in an attempt to stay cool. After it fell out of his hat a few times during a game, the officials decided it was unfair, as it could distract a batter.
As thin as a cabbage leaf is, I can't help but question it's effectiveness. On a hot day, I would think it would thaw very quickly. Even several frozen together would offer only a brief respite from the heat.
This man is now likely trying to come up with another way to get some relief that baseball officials won't take offense to, but I have another suggestion ... if the heat bothers you that much, you probably need to find another profession!