This may be a bit tangential, but at the same time there is a common confusion in terms here that might be important to frame the discussion.
When speaking of "Classical" music, many people mean "anything with an orchestra that isn't a movie soundtrack." However, in terms of music history, this is not the case.
The Classical era was a specific timeframe that began with the end of the Baroque era (which many would say is the year of J.S. Bach's death) and prior to the Romantic era, a period from roughly the mid-18th century until the early 19th, around 1820 or so. It's hard to pin down the exact dates because art doesn't simply have a wholesale change overnight. Bach is seen as the defining composer for the Baroque era but characteristics that are indicative of classical compositions started to appear prior to his passing.
Similarly at the other end, romanticism came in slowly. Depending on who you source, you may see Schubert termed a classical era composer or a romantic era composer. There are transitional periods, and that makes things slightly fuzzy.
I don't have any nonspeculative information on when or why "classical" became a blanket term for "older-sounding orchestral music." However, I would assert that much of it has to do with the fact that some of the most famous composers in Western music came from that era - Haydn, Mozart, and Beethoven (though he is also a bit transitional into romantic) most especially. When common knowledge of orchestral music rests on a set of composers who all lived during one era - considering movies like Amadeus, pop culture references like Schroeder's obsession with Beethoven in Peanuts - it's not hard to imagine how the colloquialism could have come about.
I recommend a look at the Oxford or New Harvard dictionaries of music for an easy and reliable source on the eras of music as well as the composers/musicians who developed theory and practice at the time.
If you are more curious about how the term itself came about in the first place, you may want to explore classicism in terms of art history, as it derived from there. However, that is not an area of expertise for me.
Edit: Typos
But what about the OP's original question? When (and where) did people start using the term 'classical', in either the small or big sense?