And you would think that there are enough native speakers in China to mean that there wouldn't be a group devoted to bad Chinglish signs on Facebook. So it goes both ways, right?

Actually, isn't "faliang" the actual phrase there, and not "toufa"?

In that case the translation is correct.

The translation is correct. It's just a bit confusing. 我的脑袋发冷 is a better translation.

发冷: fālěng v.o. feel cold/chilly

我的头很冷 would be more correct, tho.

I think the translation is correct and appropriate. "发" is a pretty standard way to describe conditions such as "发冷","发热","发烧". Re: the previous comments, "脑袋" is fairly colloquial and therefore not suitable here, and "很冷" only describes one condition, i.e. very cold.

I would guess that most people who read 我的头发冷 would think that it meant "My hair is cold". "My head is cold" is correct, but only when someone points it out that 我的头发冷 could mean "my head is cold" does it become apparent.

It's not good to have a sentence that can be understood in 2 ways on an ad but as this is for the benefit of Americans mostly, it does not make too much of a difference. I think the cultural connotation as shown in the Baidu search is more of an issue, as is the choice of hats which gives a very wrong idea of Beijing (how about a Mao cap?).

um. do chinese men commonly suffer from "cold penis head"? and how is it that 六味地黄丸 cures the problem?

Note that in Hong Kong or Taiwan there would be no confusion as among full form characters the 'fa' is written differently in toufa and faliang. I guess this is ad was originally written for Taiwan or HK, and then just switched into simplified characters for the mainland. (Which also explains that hat that you say they don't wear in Beijing.)
Normally such confusions are unlikely when switching from full to simple form characters (although the can more occur more frequently in the other direction), so I'd say Continental is just a bit unlucky here.