It seems like a weird choice for a draft animal.
Thor's "ride" fits with his role as god of the common people. While most of the gods ride horses, Thor drives a wagon, or walks. (He walks across Bifrost, the rainbow bridge, according to the Prose Edda.)
As for the goats, I'm just guessing here, but there's a verse in the poem Havamal, which is supposed to be the widsom of Odin himself:
One's own house is best, though small it may be;
each man is master at
home; though he have but two goats and a bark-thatched hut
'tis better than craving a boon.
So a goat would be the least that a subsistence farmer could get by with - but Thor's goats are special, because he can eat them and use them for draft animals time and again. Also, anyone who can yoke a goat and make it pull a wagon is clearly possessed of supernatural powers.
Snorri’s tale of the goats’ being being magically reconstituted after being eaten for meat is of a common type of mythic motif, a fantasy cherished by a people who know hunger intimately. (Compare Ojibwe myths featuring a tiny kettle that proves an inexhaustible cornucopia of manoomin [that’s “wild rice” to us chimooks]; a more specific match, though, is the myth of Tantalos and Pelops.) The socio-economic class associated with Thor’s cult was lower than that associated with Odin’s, after all.
At one level, one might say that even a god might have to settle for whatever species he could get with this rare magical property, if he felt it requisite. But on a very different level, one might ask if his “choice” of goats is any weirder than, say, the choice of a castrated blue lion to be the mount or “vehicle” of the Bodhisattva Manjusri. Quite possibly these pairings between divine personages and their familiar animals are holdovers from a stage of totemism.
It looks less weird in the context of a version of the Auriga mythology involving goats. Part of Auriga are the Haedi, the two goat kids.