How about Winslow from CatDog? It was established that he's not a mouse, but I don't think his true species is known.
Will comic strips count? There was Zoogie from the recently departed Out of the Gene Pool (2001-2008; renamed Single and Looking in 2007). Basically, Zoogie was a response to all the complaints newspaper editors sent to the cartoonist about his characters being ugly, so he created a furry koala/mouse like thing who was very cute but also a big jerk.
Will comic strips count? There was Zoogie from the recently departed Out of the Gene Pool (2001-2008; renamed Single and Looking in 2007). Basically, Zoogie was a response to all the complaints newspaper editors sent to the cartoonist about his characters being ugly, so he created a furry koala/mouse like thing who was very cute but also a big jerk.