The dogs do represent a sector of society, just as Squealer does but their role in Animal Farm is mostly symbolic. The dogs are representative of the secret police of the Russian Revolution. Their function is one of bodyguard and they use fear and intimidation to suppress any trouble. Even the mere mention of the dogs is enough to cause panic.
Squealer's role is far more sinister and he represents the propaganda 'department' and is likened to the Russian newspaper - the State-owned newspaper - giving out mis-information, lies and manipulating the truth. He is not overtly cruel and the animals do not fear the very mention of his name. His role, however, is far more important as, without him, there would be too many unanswered questions. He manages to cover the tracks of the pigs and persuade the animals that he is right.
Like any good propaganda boss, he is able to not only explain the present, he is also an expert at rewriting the past.