If what you want is a superb coolant, you have to try liquid helium. At about 5K absolute it is certainly cold enough. At these temperatures there are also many superconductors available that will permit you to reduce the thermal load from resistance heating.
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"Don't disturb my circles." translation of Archimedes last words
Is this for superconductors or are you trying to make standard copper winding electromagnets more powerful by (say) putting them in the kitchen freezer?
Are you perhaps trying to run an electromagnet at a higher voltage to increase the magnetic force and need additional cooling to prevent the winding insulation from overheating, melting and then shorting together?r
I am partial to liquid nitrogen (which is a much, much better coolant than Ethylene glycol), but it has its disadvantages and so is not suitable for some applications. Forced air cooling is also an option and has its own advantages, as does forced water cooling. All may be viable solutions (depending on your specific application).
Can you please provide more information on your application.