Is there any hidden meaning in “haircuts” in the analogy of Presidential election as “usual vague contest between competing slogans and haircuts”?

Use of haircut in this passage is an instance of metonymy, in which the single term haircut is used to stand for many aspects of appearance, including clothes, grooming, and mannerisms. While it represents appearance, I don't see it as representing character at all.

Occasionally one sees elections referred to as "beauty contests" or as "popularity contests", both referring to a tendency of voters to be strongly influenced by how candidates look, for example in televised appearances.

Regarding the comment by Charles that haircut is not a well-understood term for "looks" or "appearance", that's difficult to gauge. Some terms like "big hair", "newscaster hair", "bad hair day", and "news anchor hair" are widely-used in the US, and news stories about John Edwards' $400 haircut or about Bill Clinton's $200 haircut at LAX aboard Air Force 1 were legion a few years ago. But I agree that trying to summarize someone's appearance via "great haircut" or the like probably will lead to misunderstanding. It is less likely to be misunderstood if, being asked to speak in favor of a candidate, you merely mention their great haircut; almost everybody will understand that that is sarcasm.

I think the words you have italicized in your quote are basically a reference to how some voters, rather than doing careful research about where the candidates stand on important issues, are instead influenced by short sound bytes, charisma or charm, and good looks.

So, does ‘haircuts’ simply mean ‘looks’ or ‘character’? I say this kind of tongue-in-cheek, but I think you're giving the American voter too much credit by throwing the word ‘character’ in there.