The English version you quoted seems to be the NIV, which is definitely in the minority rendering. Most translations use something closer to the original, whose word-for-word order goes something like "whoever would quench one of the small ones these a cup of cold only into name of a disciple"; for example, the NASB reads "and whoever in the name of a disciple gives to one of these little ones even a cup of cold water to drink". Therefore, "little ones" and "disciples" are not necessarily the same referents.
It's possible that the NIV is simply awkward. They may have been trying to say the equivalent of "if anyone...who is my disciple", and simply gotten turned around by reading the Greek too many times. I know I've been guilty of that in my own translation work; it's easy to forget what's awkward in the target language when you're thinking in the source language.
There is no textual-criticism issue here; some source texts omit the word "only" and some add the word "water" but there's no question about the phrase "in/into a disciple's name" belonging to the text.
Now, whether the "little ones" still refers to disciples or even adults, or whether there were some children standing around that Jesus could point to, is up for grabs. There are at least 10 places in the NT where "μικρός" appears paired with "μέγας" as in "the small and the great" (especially in the plural, as in Mt 10). I rather think in context Jesus is contrasting the "great" prophets and righteous ones with the "small" ones around him.
Similarly, in Mt 11 Jesus is contrasting "young ones" (infants, or the young of animals, not "children" who can speak, see LSJ) with the philosophical and those who connect the dots.