If it's one of those single-bottle chillers, it will work just fine. They don't have a compressor like a refrigerator, but instead use some solid-state magic to create the cooling. The one I have is labeled as 5 A @ 12 VDC. That's the same power draw as 3 or 4 of your 12 V incandescent lamps.
If on the other hand you are talking about a multi-bottle wine chiller, those generally have compressors. Something like that would run, but would draw your batteries down quickly. And on a modified sine inverter the compressor could suffer an early demise.