Knights, maybe they could be like Fighters but with some political power.

Assassins. Obvious what they do, but could replace your Snake class.

Fighters could be Split into Pikemen, Archers, Swords, Cavalry. 

Torturers? For when people get captured.

Though personally I don't like the class system, we have seen with GoT that everyone needs to lift a blade at some point, and if you cant talk you way out of something you are likely to die. I think it better to have like a list of maybe 1 or 2 things you are really good at and 2 or 3 you are average at, and then as the game progresses you gain or increase your skills. This allows for character growth and doesn't make players feel tied to a class. Skills can be unrelated too, as long as it is reasonably explained in the character Bio why they have those skills. E.g. someone could be a expert in intrigue and court politics, but also a very good shot with a bow because they had taken part in many archery competitions while growing up in court.

It is of course, up to you, i'm just giving an opinion. I'm still in either way :)