Well, he’d play a Stein piano, for one. Here is a piano that Mozart played that was built by Anton Walter, based on Stein’s design.
Fortepiano specialist Kristian Bezuidenhout talks about how Mozart’s piano differed from the modern piano here.
Beethoven owned a number of pianos. Here is an inventory.
Parts 3 and 4 feature bagatelles, part 5 contains Beethoven’s Fantasia Op. 77.
Chopin played a Pleyel (No 13819 in fact) from 1848. He said, “When I am not in the mood, I play on the Erard piano, where I find the ready tone easily. But when I am full of vigour and strong enough to find my very own tone – I need a Pleyel piano” Check out these offerings from radiochopin.org (Chopin fans, your weekend is now planned) on Chopin’s Pleyel, Erard. and Broadwood pianos . Here is Chopin’s Pleyel piano.
Here’s a historical recording of Raoul Koczalski playing Chopin’s Pleyel (year given here as 1847) in 1948 in Warsaw.
Want more? A show in Howard Goodall’s BBC Big Bangs series is devoted to the history of the piano. I own the series and recommend it (available for purchase at the usual venues). I would also like to recommend his Story of Music tv series (from the paleolithic to the present!), but sadly, the BBC has not made it available for purchase at this time. Clips from the series can be seen here. It is, however, available in book form.