Probably too low - it won't hurt it per se, but your yeast will likely go dormant. If you know your yeast type, look it up online and find out the preferred fermentation temperature range. Generally ale yeasts prefer room temperature or slightly lower (like 67-72). Don't go too high above room temp or you'll get some off-flavors.
Same thing goes for when you are bottle conditioning your beer. Keep them at room temp the first week or two. If kept at too low a temp they will go dormant and not process the bottling sugar, resulting in flat beer.
If you haven't already, check out www.howtobrew.com and check out the fermentation section. The author goes into great detail about the science of fermentation, how to do it, as well as how to avoid problems.
I all depends on the yeast strain!
I used to ferment with Cal ale at 60, but it would underattenuate, at least for me. I bet others have had success with it at low temps. If you are using an English strain it will most likely flocculate, they are pretty sensitive to temperature fluctuation. A good strain to use at lower temps is German ale, it will give you clean, lager like ales, if you don't mind the minimal esters.
Other than that, you have to experiment and see what works well, if it works for someone one way it might not work out the same for you. So give it a try and see what happens.