And on the mountain1 there lives a beast that resembles an ordinary white dog with a black head that takes flight when it sees a human. The sound it makes is simliar to the pronunciation of its name.
1 Long Hou Mountain (龙侯之山 lóng hóu zhī shān)
The name Tian Ma is somewhat misleading as the second character, 马 (mǎ), means horse. This, and the fact that the winged-horse from Greek mythology, Pegasus, is also translated to Tian Ma 天马 in Madarin, means that the two are often confused. As a result, you will often see the Tian Ma of Chinese mythology mistakenly depicted as either a horse, having wings, or both. And though it is possible the Tian Ma had wings, it is not written in the original text and therefore (in my humble opinon) shouldn't be assumed.
Perhaps the Tian Ma was thus named because Tian Gou (天狗 tiān gǒu) - where Gou 狗 means dog - was already taken.