I think that the definition of pseudoscience is "some theory which claims to be scientific and have scientific foundations, but it isn't" or at least this is my idea of that word.
So, astrology doesn't claim to be scientific and horoscopes don't claim to have scientific foundations, therefore can not be considered pseudoscience, but just non-scientific.
Pseudoscience is when your experiement cannot be replicated and is not falsifiable.
Astrology fails in both. miserably and right off the bat. The gravitational pull of the doctor giving birth to you is greater than any other planetary alligment at the time of your birth.
You see? Highschool physics can toss out of the window any spirtual crap
Bothe Western and Eastern astrologers persistently claim that it is based in science.
Also, Hindu astrology was forced to become University faculty in India despite large protests of scientific community in India.