The electrical resistance of various metals varies with temperature. This is how electrical thermometers work and in fact how many heaters are self regulating. For copper the colder it is the less resistance there is. Until you get to a point at extremely cold temperatures where the resistance is zero. So you can send a current through the wire and there is nothing in the wire stopping it. It does still build up a magnetic field which stores the energy and can be used for various other things but you can maintain this magnetic field using very little power.

Of course this is not the entire truth, they do not make the magnets superconducting to save on the power bill. The problem is that any energy that is lost to electrical resistance gets turned into heat. And with the amount of current they need for the huge magnetic fields they need the amount of heat generated by any resistance is enough to melt the copper conductors. The Large Hadron Collider did this during an accident, called the quench incident. It was caused by a bad connector between the magnets which had a tiny bit of resistance. This caused the entire thing to explode in huge ball of green and blue sparks. Green was the vaporized copper and blue was the helium plasma. There are no footage of the fireball but there are images of the aftermath. So best keep those magnets cold and superconducting.