Welcome Hairless.
The answer to your question depends some what on what you mean by Wine Cooler.
There are several post on this forum from over the years concerning using a freezer or refridgerator to reduce the temp of the wine during several steps of the process.
Even more information on whys and hows can be found on beer forums; as maintaining less than typical ambient temps are important in several types of beer processes.
For wine making the most use is for cold stabilization. (Process of reducing temp to 30-40 deg to cause tartic acid to fall out as crystals prior to bottling).
There may be some benefit on some wines to hold temps in the 55-60 deg range during bulk aging.
For long term storage of wines, (bottling aging), (like a poor mans wine cellar), there are differences of opinion. Even though some folks tend to consider thier opinions as gospel fact.
In my opinion the possible advantages of using a freezer for long term wine storage are out weighed by the disadvantages.
Use of a external temp controller works by controlling the power to the unit. This results in wider than normal temp swings, (not good for wine aging), and the unit not running a efficently as designed. Some comments on other boards also raise a concern of limiting the normal life of the freezer by doing this. There are also some strong opinions by a few that the vibration from the compressor will prevent the wine from settling and aging properly.