Snake's appearance, with his unshaved beard and uncut hair, has been directly referred to as the long-time manga/anime/literary staple of "無精髭 bushyouhige" and "無精髪 bushyougami". Roughly "no energy beard" and "no energy hairstyle". I am not the one who's saying this, by the way, Director Kojima was the one who explained this about Snake's appearance. Frequently, at the beginning of the release of MGS2. The unshaven beard and uncut hair image was done purposefully to represent Snake's temperament of not caring about appearances because he doesn't care much about the details of life. And the "無精 bushyou" thing is always used to represent a bachelor, who since he doesn't have a girl to worry about, is free to let his appearance go wild.
The concept of "mullet" actually doesn't exist in Japanese culture, as far as I have ever known. The term in fact does not exist in the dictionary. It kind of exists in the form of "ムレット muretto" and "マレット maretto", which spelling being the standard one is not agreed upon, or cared about for that matter. It simply isn't a relevant enough subject.
There are some non-Japanese people who think that what's known as the "ウルフヘア wolf hair" is a mullet, but it is actually a different hairstyle. Similar, but different.
So what Solid Snake has is the "無精髪 bushyougami/energyless hairstyle", and not the "mullet".
