"That cold it is supposed to be froze."
<chuckle> Not when properly installed they certainly won't. We have frost free hydrants here, and -40F weather doesn't affect them in the least.
Thawing it will be a bit of a challenge in that cold. I had one improperly installed here, but it froze in the upper half, so pouring hot water over it thawed it out right away. I'd try it, because if you're down below your frost line, I'd have trouble believing that it froze down low. You may also want to put hot water in a squeeze bottle and force water up the spout and down the tube. As someone mentioned, unscrewing the head will likely damage the valve down in the ground.
This summer I suspect you'll need to pull that hydrant. Either the drain back valve is non-functional, or the hydrant wasn't installed properly. These hydrants need to have coarse gravel or rocks around the drain back valve so the water has someplace to go. It doesn't drain back to the water line, but rather "leaks" out to the surrounding soil. If the soil is too compacted, the drain back won't occur quick enough and the hydrant will freeze part way down. The drain back also must be installed below the frost line.
Good luck. Nothing worse than water problems at -30 or -40. Had the bulls get mad at one of my water bowls this year at -40 and they tore it all apart. That was a miserable job.
Rod