Harthouse is a well-born young guy who is trying to get into Parliament. He's in the same political party as Gradgrind. He comes to Coketown to learn how to work the political process and get to know some money men like Bounderby. While there, he tries to seduce Louisa and almost succeeds. After she runs away from him, Sissy tells him to never show his face around town again.
Of all of these guys, Harthouse is probably the one whose personality we can most easily recognize. Outwardly, he is all handsomeness and gentlemanly good manners. He has the kind of slick, smooth social ability that makes him instantly likable. Inside, his whole M.O. is to talk everything down. His philosophy of life is that everything is worth nothing, and that there are no honest people. Basically, he thinks that caring very much about anything is a big old waste of time. It's a measure of just how lost and confused Louisa is that this kind of nonsense really appeals to her.
In a way, Harthouse is just like Tom: both use the absence of morality to justify their own bad behaviors. Though the actions are different (theft on one side and attempted adultery on the other), the attitudes behind these actions can be easily covered up by Utilitarian thinking. To Dickens, the main problem with an economic or statistical approach to figuring out how people should act is that people who are prone to doing bad things will be able to excuse all sorts of awful crimes. All they have to do is talk about life as a numbers game. Characters like Harthouse are a handy way of showing this problem.