The next time I'm in Budapest...
Preparing game can be a real challenge. For example, you should never handle wild meat without wearing gloves. Each species has its own preparation rules. For most people, it's simpler to frequent a restaurant specializing in game, many of which are Central European. Enjoy!
In addition to the wines mentioned in our food pairing table you might consider a Cabernet Sauvignon, Malbec, Spanish Tempranillo, or a Zinfandel.