He doesn't really get any scenes where he gets to talk about himself directly, and it doesn't help that it's already been confirmed at least one of the scenes that got cut from the final movie was about him. Hopefully we'll get it in the BD. But I wouldn't quite say that he has *no* personality beyond being a woobie. I got the impression both from his dialogue and his body language that he's tired, cynical, and generally really cranky about his lot, but determined not to give up for Steve's sake. He seems like the grizzled vet who's always thinking "are you kidding me?" It works as a good setup for Bucky Cap if they go that route, and at least it's more to work off of than poor Rhodey.