It should be observed that the character of Mickey Smith actually holds up a lot better in hindsight than he seemed to at the time, because now we have the benefit of seeing the entire picture. The problem with his character is that he seemed far too one-note and played for comedy. He was The slightly-loser-ish left-behind boyfriend who wasnt as good as The Doctor. And to be honest, for a lot of those first two seasons it wasnt entirely clear is we were supposed to be laughing at him or feeling bad for him. Possibly we were meant to do both. And this moment in The Girl in the Fireplace both underscores that problem and marks the beginning of its resolution. The reference is to a horse named Arthur, for those who didnt recognize it. The Doctor finds Arthur the Horse on a spaceship (as one does) and clearly has his heart set on keeping him. Rose firmly tells him he cant (although what authority she has to make that call is beyond me) and The Doctors retort is that it isnt fair because he let her keep Mickey. Yes. The Doctor equates Mickey Smith with a horse. He sees him as Roses pet. Its funny because its an odd juxtaposition, but its also a little sad. And it marks a definite step along the road to Mickey setting out on his own shortly thereafter.