The game doesn’t say; this is beneath its abstraction level.
Basically, the game assigns all items a weight which represents how much it encumbers you (and in some cases, an item’s “weight” is higher than its actual physical weight, because it is particularly cumbersome). Then you have a limit on how encumbered you can get before being penalized, based on your Strength.
The game does this because it is quicker and simpler than trying for anything more “realistic” (though actually, many players ignore even this because it’s still obnoxiously fiddly and time-consuming to track). This is what is known as abstraction, and it’s an important part of any game.
Thus, the game does not really care how or where you store things. You can have bags, or not, as you like. There are limits on how much any one bag can hold, but not on how many bags you can have. Your DM may put a halt to particularly ridiculous amounts of them, but that’s purely up the DM.
So in short: the game doesn’t really care whether or not a centaur has saddlebags. Ask your DM; I doubt it will be a problem.