The cause of this structure in Spanish is because it is pro-drop, which is to say the morphology of the verbs is sufficient to deduce the subject, sufficient to allow us to "drop" a pronoun we might plan to use.
Es feliz tells us not only that the subject "is" happy, but also that the subject is singular third person. If instead it had said soy feliz, we would know both that the subject was happy and that the subject was in fact the speaker. The same for quiere, not only that the subject wants something but that that subject is singular third person. This allows use of a generic type of subject that isn't overly exact or specific, which you describe as "impersonal."
Outside of certain irregular verbs, English verb conjugations don't change very much with person or number, and so we cannot derive the subject from the verb form as Spanish speakers can. So we need to state it specifically, even when there really isn't one, in sentences like "it is raining." or "it is time to go to bed" there really isn't a subject, but English needs us to create an artificial one.
The closest we can come to your sentence in English is to use an impersonal pronoun "one" which is generally considered old fashioned, or to use a different subject that conveys the right general meaning.
One is happy when one wants to be.
People are happy when they want to be.