@Isamu Akai; @Werdnae;
The idea was seems adapted into Yellow from Ash and Pikachu's forming a bond of friendship, and there was no official reference to happiness either. It was referenced more as friendship by the original friendship rater, with terms like "happy" and "trust" being used as a descriptor. Seeming happy after a hair cut is just that, you got a nice hair cut, and as such, feel happy. However, actual ratings of the value seem to reference friendship more.
This gives the happiness quotes of the first raters. If you look at each word in isolation, you see happiness mentioned more but it does not explain why the concept is not mentioned in all phrases. However, looking at the context as a whole, all the sentences describe the evolution of a relationship from stranger to friend. At it's highest value, happiness is only incidental to the closing phrase "It must love you a lot!", which is the polar opposite of the phrase for the lowest value "It doesn't seem to like you at all. It looks mean." Note how this final sentence says it looks mean, an emotion, despite its opposite valence, is on a completely different dimension than happiness (one can simultaneously be mean and happy). The following terms demonstrate how this relationship unfolds. It goes from "not liking" to not being used to the trainer, to trusting, and in the end, loving. The concept of happiness does not go through this evolution across terminology. Though, I do wonder what being cute has to do with anything than being uninformative midpoint (in terms of the midpoint value being located within this phrasing).
So yeah, as far as I am concerned, its always been a friendship value confounded with the term happiness. You can say the term happiness makes more sense based on some anecdote, but when you look at the actual terminology used across multiple raters, the concept measured is the relationship between humans and Pokemon (or in simpler terms, the friendship between them). Really, when you look at the major theme in the franchise (i.e., friendship) one begins to wonder why the term happiness persisted for so long other than nobody raising the point earlier.
Apologies for the awful, awful commentary but: http://www.youtube.com/watch?feature=player_detailpage&v=uoo4XY2824Q#t=434s
"You should just keep it with you. That should make it happy! You can talk to it and see how it feels about you."
So happiness was mentioned once, but this was in reference to keeping Pikachu outside of its Pokéball. The last sentence however, is the one of interest as it directly refers to the act of checking Pikachu's "happiness". It didn't say that you should talk to it to see how happy it is, but instead, to see how it feels about the PC. This last part is exactly what all the Friendship Raters and Dr. Footsteps do, examine how the Pokemon feel about their trainer.