Optimal temperature ranges vary slightly yeast to yeast. So a check with the yeast supplier will help with that data. But for most Ale yeast getting below 60F is probably too low. Maybe you still get fermentation, but the lower the temp gets for most ale yeast the cleaner it ferments. So if your making something with an english ale yeast, you might miss out of some of the intended flavors that strain makes.
When temperature drops too much for the yeast this can signal them to start to flocculate out prematurelty. Again, certain english strains flocculate so well that reheating the fermentor may not be enough to get them active again. If you suspect that the yeast has significantly started to floc-out due to low temps you'll need you rouse them manually.
You can rouse yeast with a sanitize racking cane and stir a bit, you can literally swirly the fermentor some if you have enough head space to do it. Some brewers with access to pressurized CO2 (from a kegging setup) will actually blow CO2 through a racking can into the cake to get the yeast up again.
If you do need to rouse your yeast you should warm up the fermentor first, then do the rousing. Otherwise, the yeast will settle right back out and not "wake-up".