Well, I suppose you could sand the varnish off if you didn’t like it very much . . . but, realistically, I don’t think it’ll affect the wine that much. If you’ve read some of my pieces on smaller barrels you know that the smaller the vessel the higher the ratio of air exposure to wine volume anyway, which I wager would make up for loss of porosity. You’ll probably get quite a bit of oxygen ingress around the bung as well as every time you open it to adjust free SO2 (something you should be checking on monthly). A word to the wise, however: Sometimes smaller barrels carry their own problems, like they’re just “for show” to keep on top of your bar, or have been sitting around in a warehouse for far too long so they’re all dried out. Even if it was given to you as a gift, see if you can find out more about where the barrel came from, what kind of wood it’s made from, and how long the store carried it before they sold it to your gift-giver. Then you’ll have a better idea if it’s going to be the kind of vessel appropriate for proper winemaking and proper wine aging (note that some novelty barrels are charred for aging spirits).
No matter what, you should clean it thoroughly with very hot water and, if you have it, soda ash or sodium percarbonate (peroxicarb). Fill it up with hot water first to see if there are any leaks. These small barrels just don’t sell as quickly as standard sizes (like I said, they’re often seen as decorative pieces only) and so might not be as well made as a regular wine barrel from a producer you trust. If, upon first filling with hot water, you get a lot of leaks that don’t stop once the wood gets wet and swells up, it might be better to just keep it as a decoration for your bar. If it’s very dry, a small barrel can be placed in a laundry sink and submerged as well as being filled up to help the wood rehydrate.