A horoscope is a view of the hour. It's a graphical representation of the sky for a given date and time at a given location. I used to cast them for our astronomy class' star-gazing outings.
I studied astrology for a couple years while in college. I got started mainly to find out why, when asked my sign, my response would cause them to back off cautiously.
Astrology, as it was taught in the early 70's, is a kind of theory of personality development and interactions. It is very rich in symbology and elaborate in its internal logic -- as theology is, though astrological theory was much less rigorous in its logic. There are at least 10 components to a personality, as represented by the ten planets (that terminology includes the Sun and Moon), so the popular "daily horoscopes'" efforts are immediately suspect, taking into account on one of ten components (albeit a major one).
I came out of the whole experience with an exceptionally strong skepticism of any elaborate system of beliefs based entirely on internal logic (regardless of how elaborate and rigorous) but with no means of objectively testing the conclusions reached through that internal logic. By analogy, it's kind of like navigating by dead reckoning. You use your heading and speed and elapsed time to extrapolate your position, but unless you can get an actual fix on your position (eg, shot the stars, consult the GPS) then you are going to drift off course and the longer you've been doing this the farther off you'll be. This is especially true of systems of belief that make pronouncements about the supernatural.