The cooling units I’ve looked at require a direct vent and strictly prohibit forced discharge air (duct work).
As far as the wood is concerned, no, it will be just fine whether it’s sealed or not with the most typical species found in cellars being untreated redwood. The reason being is wine coolers serve the same function as wine cellars. They maintain a steady state environment for long term storage of wine. With fine wine that a person wishes to cellar for several years, it needs a stable temperature of about 55 deg F and a relative humidity of around 50%. Temperature fluctuations are what destroy a good bottle of wine, and the humidity is what keeps the cork from becoming dry and cracking. Once the cork cracks, the bottle will leak and the wine will be exposed to oxygen. When this happens, you’ll get a nice expensive bottle of vinegar.
As far as beer is concerned, I love a good micro brew, but I drink it too fast and there’s no need to cellar it.
My favorite drink of all time, is called “FREE”.