The honest answer is that there is no commonly accepted word for the study of calenders. It's clear that the question relates to how societies perceive and describe the division of, and the progression of time. This involves in all cases the study and measurement of natural periodicity (astronomical generally) and in most cases is combined with the study and ordering of events (usually human or geological). For example the Roman calender measured time in years (astronomically-based) passed since the founding of Rome (event-based).
The science of the measurement of time is 'chronometry' (from the Latin/Greek words for 'time' and 'measurement') while the study of the ordering of events is 'chronology'(from the Latin/Greek words for 'time' and 'description'. A candidate word for the study of both might be 'chrononomy' (from the Latin/Greek words for time and arrangement). The Oxford English Dictionary recognizes 'chrononomy' but describes its (historical) use as rare. Hovever this only reflects the fact that the study of calendars is a very modern interest.
'Horology' comes from the Latin/Greek words for hour and description, but has come to (generally) relate to the study of mechanisms for measuring time. It has to be said that the Greek word here also included a sense of seasons and time generally, but the Latin word definitely relates to hours.
Calendar comes from the Latin word Calends, meaning 'call' or 'proclaim', and used uniquely in Rome in relation to the first day of each month. The first day of each Roman month was a day on which announcements would be made, and accounts would be calculated from. Strictly speaking then, the word 'calendology' would mean something like the study of proclamation descriptions. Words, however, mean whatever we mean them to mean, and 'calendology', or 'calendarology' might work for us, even if the philologists shudder at it.