Having only played on a modern piano, I can't even imagine how this is possible..
Piano design didn't really mature until around 1850. So a lot of the most famous classical piano music was composed on not-quite-there yet prototype instruments with a thinner and less powerful sound, and sometimes also a less sensitive action.
My gf had to play a vintage antique fortepiano in a production last year, and the solo sound is closer to a fat harpsichord with better dynamics and slightly random tuning than a modern piano.
It's what Mozart, Beethoven and Haydn would have played: they literally never heard their music on a modern instrument.
This is really apparent in the first movement of Beethoven's Moonlight Sonata. In the original instructions, the pedal was to be held throughout the entire piece. On a piano of Beethoven's time, that would lead each chord to blend into the next without overpowering it. But if you try to do that on a modern piano, the tones are sustained for so long that all the chords get muddled together and the result is a mess.