definitely not easier to do it when the car's hot, but definitely easier to take the nuts off the studs after you spray/soak them in PB Blaster for 10 minutes.

i don't know how much clearance you have to get a drill in there with a bit to drill into the stud so you can extract it, but definitely get yourself a punch so you can center the hole you're going to make into the stud that way you don't mess up the threads/head. if you have room for the drill then give it a shot, but if you have enough stud hanging out of the head to get some vise grips on it after you remove the manifold again, I'd probably just eat it and take it back off.