How do you know if it's "the good horse's master" or "the master's good horse"?
aaeksio ends in o anyway, but horse ends in -e in the nominative. Because horse ends in o it is in the genitive.
"The master's good horse" would be Sȳz anne āeksiō (or, more likely, Āeksiō sȳz anne).
Why is the master taking the genitive case if the owner in this sentence is the horse??
Āeksio just happens to end in -o in the nominative (the genitive is actually āeksiō with a long o.) See previous comments for further discussion.
It doesn't matter if it is good or glad
wouldn't this be the master's good horse is glad? Does it mean the same?