The phrase "are in the saddle" is an idiom that means someone is in control or in a position of power. There are various synonyms that can be used to convey the same meaning such as "are at the helm," "are in charge," "are in command," "are in power," "are at the top," and "have the upper hand." These phrases can be used interchangeably depending on the context and the speaker's preference. They all indicate that someone is leading and in control of a situation, making important decisions and directing others towards a certain goal.