I would imagine that is too cold.
However, the temp of the water doesn't matter. It's the temperature of the beer that's important. Though in my cooler I have found that the temp of the water is usually very close the temp of the beer - within 2-3 degrees.
So I can't really offer you a clear answer, but if your ale is below 60 you are almost certainly going to have issues fermenting out completely.
In Process - Russian Imperial Stout, Nelson Sauvin Rye IPA, Mild No.3
In Kegs - Barley Wine, Apfelwein, Wild BlackBerry Wheat, Coffee Oatmeal Porter
Gone - so many :(