Horace, or Quintus Horatius Flaccus as he is known in Latin, wrote in Classical Latin.
He lived 65–8 BCE, whereas the era of Classical Latin is considered to be roughly 75 BCE–300 CE.
As his entire life falls within this period, he should be considered a classical writer.
Horace is among the most highly esteemed writers of ancient Rome.
You could well say that he is one of the reasons this era is regarded classical.
The classical era is often defined so that it includes the authors we want to consider classical, this is a case of chickens and eggs.
However you interpret things, it seems uncontroversial by any definition that Horace wrote his works in Classical Latin.