It's absolutely possible to do so. The main thing you have to watch out for is oxidation.
A bottle of wine, once opened, is going to be consumed fast enough for oxidation to not be a problem. A cask/barrel will not (unless you're a true champ at drinking wine). The trick is to introduce an inert atmosphere above the wine as it's dispensed at low enough pressure to not dissolve too much of the gas in the wine. Wineries using this practice during aging employ very-low-pressure nitrogen gas systems (see some examples here). Nitrogen's not really accessible to most homebrewers, so you'd have to make do with a CO2 setup at low pressures to do the same thing.
With bottom-tap kegs, you could try either running an existing CO2 regulator as low as it can go, or using something like a cask-breather, typically used for preventing oxidation when serving cask or real-ale style.
With the top-tap kegs, you'd have to see how much pressure you need to dispense. If it's too high, you might pick up carbonation in your wine. So this might not be a great option.
Hope that helps out a bit.