The other wiki is called wikiFur...guess what it's about.
A bit of searching (with carefully chosen lingo - using 'flight' itself typically calls up air travel sites!) yields several pages on the very basics. According to this one, drag, lift and thrust are the three important components we have to consider. Lift and thrust are what help get an animal airborne, whilst drag provides a barrier to flight. Lift can be increased by the shape of the wing and the speed of the animal, and is opposed by its weight. Thrust contributes to the speed of the animal, as it is the force the animal produces against drag. In order to move forward, the thrust produced must be greater than the drag that opposes the animal's movement. In winged animals, thrust is produced by the flapping of the wings, which can require a high power output from the animal, i.e. greater muscle power. And muscle power doesn't increase in the same way that drag and weight does.
Now, Arabian horses are meant to be one of the light breeds, and they typically tip the scales at 800-1100 pounds (source) - that's about 360 to 500 kg. According to the above, they'll need to be able to generate a lot of lift to oppose their weight, more than their wings can possible do from a standing start. Yet, in episode 7 of RxJ, that's precisely what Siero (I'm basing this romanisation on what I remember of Italian - the letter 'c' gives a hard sound) does, with Romeo on his back, no less.
But yes, the wiki site...I found the following page on Pegasi, and just had to remember it somehow...
p.s. IIRC, the third Harry Potter film got it right, what with Buckbeak taking off at a run..