Yes, but also due to the changes in piano construction.
In some ways, a classical piece played on a modern piano might sound more true to the composer's original intent than the piano it was originally played on. Modern pianos are generally louder and brighter than the ones in the late 1700s and early 1800s. So loud passages, such as might be found in some Beethoven, may actually be taking advantage of the power of a modern piano in a way that Beethoven might have enjoyed and/or intended.
Regarding temperament, there we are hearing something different from the composer's original intention. Luckily, with digital sampled pianos and virtual instruments, we can easily see what pieces might have sounded like in the time of their composition, and it's fascinating to hear the subtle differences that come out when you change the pitch and temperament of a virtual piano.
In addition, some pianists have their acoustic pianos tuned to historic tunings (also harpsichords and clavichords). Obviously the downside is that you can only re-create one historical period at a time, or even really one composer's favorite tuning at a time. And there are re-creations of period instruments that are much closer to the original sounds and tunings of the pianos from the times that they reflect, for the ultimate in authentic sound.
I just realized you're not only talking about keyboard music. Orchestral music is a whole nother kettle of fish.
Temperament is a lot more fluid in an orchestra playing without a piano. Yes, the strings of the strings section will be tuned to ET 5ths, usually, and generally the whole orchestra will play with a modern pitch reference (e.g., A 440). Also, world class musicians will often have a good enough pitch sense that they will play notes very close to equal temperament, if not right on. But they don't have to. With a keyboard instrument, you pick a tuning and that's what you've got until you pay for the tuner to come around again. With orchestral instruments, they can change intonation on the fly.
How precisely an orchestra plays to a specific temperament can vary from orchestra to orchestra, and even from piece to piece. A conductor/director could request all thirds to be played slightly sharper or flatter, for example, and a world class orchestra can almost certainly accommodate such requests. So we might be hearing tunings closer to the originals that you might think - as long as there are no pianos (such as in a concerto) or harps around.
That said, once again some instruments have changed in their construction and timbre since the 1700s. Particularly I'm thinking of French horns, but other brass and woodwinds may sound more powerful than they used to.