thats a bit short sighted i guess.

Classical music has a longer period then that,
started with church music in the 9th century and develops throughout history.

around the year 1000 polyfonie was developed witch had a big influence.
in the Renaissance the printing system was developed witch made it possible more people could learn how to play.
around 1600 Barok comes up, music changes from lyrical to instrumental.
the european kings and queens got more into music and just hired those guys to write them some tunes. They kinda fought eachother with who had the best music ( better then fighting with swords )

the period that provides the name classical ( classicism period 1750-1810 )
the one you talk about, was a very short period. Mozart and Haydn ( some say Beethoven as well ) where this period, they started to add the little notes to the scores f=force p=piano that stuff.
Austria became bigger and more important in europe around that time, Mozart and Haydn where also called the first viena school.

Then the romantic period came, musical peices became longer, more complex, more instruments etc.etc.

it takes a huge book to explain european history in its relation to music,
for example, if the church wasnt located in italy in the beginning it all could have looked different, if it was in spain a lot of music would be in spanish etc.etc.etc.

its all about action-reaction