Not to be confused with "whorology", which is the study of my ex-wife.

That's worded poorly. I guess literally it translates as the "study of time" but physicists study the concept of time, and nobody would say they're doing horology. If you read on it explains it's the study of the measurement of time in general but horology has specifically come to refer to mechanical timekeeping devices. Watch and clockmakers are horologists, watch collectors may say they're "into horology."

It is like horoscope in that "horo" refers to time. Horoscopes are the "study" of the time of a person's birth and how that affects their life or whatever.

Whereas the study of thyme would fall under horticulture

Not quite. From the very page you linked to:

"Horology is commonly used specifically with reference to the mechanical instruments created to keep time"

Horology is generally used to refer to watchmaking/clockmaking, just as a horologist is a term to used to refer to watchmakers.

The main term for the Wikipedia page you linked is Chronometry, and that would be the more correct term to use when describing the study of time. There's even discussion on the talk page about how it was probably incorrect to have merged the Chronometry and Horology pages, but edits haven't been made to fix it yet.

Have you never watched pirates of the Caribbean?

A clock >> horloge

I had never heard the term, but I started reading a book this morning that calls a time piece a horologe.

Just remember not to say it with a silent 'w'

A horologists is a clock maker

Horoscope = time + watch. I guess, from the claims that you can see into the future with it.

Whorology is the study of whores. Notable practitioners include Donald Trump, who, unusually, decided to marry a few.