How many words are in the Latin language total? There are many, but I am curious to see how many. More or less than English?
This is not likely to be the final answer, but I hope it might give some rough idea of the scale we might be talking about.
Perseus has a tool for studying word frequency, based on 301 texts (from Classical Latin authors to religious texts, e.g. the Vulgata). I did a search and, based on a list of 174 texts (see bottom of page for list; not sure why not all 301 were included), the total number of words produced were 6,321,361. Now, a quick look at the list shows that not all declensions are in the list. For instance, the list includes tulerit, tulerunt, tuli, tulisse, tulisset, and tulit, whereas there are many more declensions of the corresponding verb (in the active present) missing.
So, the number above is well below the "true" value. But I hope it gives an idea of the scale we might be talking about, i.e. millions.
PS: I have a question elsewhere that might help to produce a more accurate number, based on Wiktionary.
The Oxford Latin Dictionary has about 40,000 entries, according to its Wikipedia page, so that's probably a good estimate for classical Latin. Du Cange's Glossarium Mediae et Infimae Latinitatis has about 90,000 entries, according to this website. That should include most words up through the 19th century, though certainly not all words.
It's unclear to me how many Latin words have been coined since then, as proponents of "Living Latin" regularly coin new words for modern objects and concepts.