Will brown ale (newcastle clone with dry windsor ale yeast) ferment an 60 degrees? Should I keep the beer in carboy a few days longer over two weeks because of the low temperature, or raise it to 65? What will make the beer taste better?
It's not really a function of the beer style. It's the yeast strain that matters. I have not used the yeast you used, but I suspect that 60°F will work just fine. The fermentation activity will raise the temp - probably up to 65-66°F - which is right in range for most ales. It may be a tad slower at this temp, but nothing too noticeable. 2-3 weeks should be plenty of time for this to turn out well.