Little is known about this stallion's history, although it appears clear that he's able to get around somehow. Not only to places all over Equestria, but in different eras in flashbacks as well. From fan speculation, he appears to look like the 10th Doctor, dubbed "Doctor Whooves". The writers officially adopted this name, however due to copyright infringement laws he's been given the name "Time Turner".
Not unlike many background characters in the show, Time Turner has heavily attracted attention from the fans. Especially due to his supposed relations to "Doctor Who". Little evidence supports this theory that he is in fact the Doctor though, but evidence occur very frequently... Including in variation covers of the comics.
In many situations where a mass panic breaks out, or even occasionally when nothing appears to seem wrong, he's been seen running or being chased by some creature, in one instance a Parasprite swarm, in another; Changelings. He's also been seen as a Pegasus in one occasion, instead of an average Earth Pony like he normally is. Not only that, but in the episode "Over A Barrel" he appears to be a young colt, running away while wearing an ill-fitting top hat...
Although most likely being generically used as a background pony design, in cannon he either was all of these things or they're all identical individuals. He's even appeared to have multiple copies of himself in the same crowd, too. He may perhaps have identical doppelgangers, or he could have just as easily been visiting the same timeline on multiple occasions.
In several cases, his actions could be directly linked to references of the Doctor. The most noticeable of these instances includes him being part of an apple cider making contest, where he wore a tie and kept timed the contestants with a bizarre hourglass device. Possibly a timey-wimey detector.
Another, possibly the biggest nod to him being the Doctor yet, it the variation cover of My Little Pony: Friendship is Magic #2, where he's wearing a familiar looking scarf and holding a fob watch, while a menacing looking Pegasus statue looms his direction in the background. The lamp post he's standing near also resembles the TARDIS. In issue 8 he is seen holding a Sonic Screwdriver and trying to get it to work as the Nightmare Forces attack Ponyville.