Okay, I'm gonna give this a bit of a shot, since I have nothing else better to do with my time.
First off, going by the calculations, Articuno should have a good AP advantage, with it having at least a third of the AP of Lugia, which is approximately 3.82 teratons, whereas Doctor Fate scales from Injustice Superman, who shook the surface of Apokolips, which caps out at around 1.06 teratons. Of course both should be higher than this, but it serves as a good baseline.
Now, assuming that speed is equalized considering the current speed difference makes this a ridiculous speed blitz for Doctor Fate, this should be a fairly good match. Fate's levitation should equalize with Articuno's Flight, and he's faced off against characters with an ice motiff before, namely Sub-Zero and Captain Cold. Articuno's ability, Pressure, means that Fate will be tiring out twice as fast as well. And after using Hail, Snow Cloak will be a godsend, being able to hide in the flurry and striking him whenever it can. Unfortunately, Frostbite likely won't come into play at all, since Fate likes to play the range game more often than not.
Unfortunately, despite the AP difference, this is where things start to look sour for the ice bird. Since Fate's range is far better than Articuno's, and he access to both Fire and Electricity Manipulation, this means Articuno is in for a world of hurt. And, again, while Fate has fought characters who use freezing cold to their advantage, Articuno has never fought anything like Fate before. And with his Teleportation, Portal Creation, Forcefield Creation and Dimensional Travel, Doctor Fate will be too hard for the bird to hit, and even its AoE attacks will become useless if he constantly dips out of range.
Overall, despite the initial advantage, I'm going to have to give this to Doctor Fate, due to his varied means of evasion, knowledge in dealing with similar threats, and better range game.
Winner: Doctor Fate