Or is it okay for the secondary fermentation to be colder than primary?
If all you're doing with the secondary is conditioning the beer, i.e. letting the flavors develop and whatnot, it can be cooler. If you're trying to let the yeast continue to ferment out the last few gravity points, it's best to leave it around the same temperature. If the yeast are fermenting and you drop the temperature, they could fall out of suspension and you'll have a stalled fermentation.
The suggested fermenting temperatures really are to create optimal conditions for the yeast to thrive in your fermenter. I usually let the gravity ferment out first before racking to secondary where it basically conditions. When racking, I leave much of the yeast sediment in the primary because it has done its job.