Are all FreeCell games winnable?

Almost, but not quite. FreeCell is winnable far more often than most solitaires because all 52 cards sit face-up from the start, so you can see everything and plan the whole game before you move. The version that shipped with Windows used a fixed set of 32,000 numbered deals.

In the 1990s a volunteer project set out to solve every one and cleared all but a single deal, number 11982, which has no winning line. That works out to 31,999 of 32,000, about 99.997%. A later research solver measured FreeCell on random deals at roughly 99.999%, landing in the same range. So nearly every FreeCell deal can be won, just not literally all of them.