I do not like the word “determine,” as it sounds too much like “deterministic,” which in my mind Astrology is not. Instead, I like to think of Astrology in the following manner:
A Horoscope is a snapshot of a moment: hence it represents the Energies manifested at that moment, I.e. the powers of the planets relative to the astronomic features (the Signs) and their reflection on Earth (the Houses).
Hence, a Horoscope does not predict the future so much as describe the Energies at work at the moment the Horoscope was drawn up.
However… the seeds of the Future are sown in the Present, hence it ought to be possible for an Astrologer to make a prediction along the lines of “this is what’s likely to happen as a result of these forces if nothing happens to change them.”
As far as I know, Astrology does not claim that the future cannot be changed. Indeed, the highest goal of certain ancient mystery teachings was to deliberately transcend the forces described in a Horoscope – I.e. to achieve true Free Will in spite of one’s planetary influences.
Answer to How can a horoscope determine ones future? by Alex Sumner