When and how was water (in ice or any other state) first observed outside of Earth? What is the high-level chronology of this discovery, and how did the scientific community first reach reasonable consensus about it?
Mars polar caps were discovered in 17s century from the beginning it was speculated that they consist of ice (later observations confirmed that they are 70% water ice). The evidence of presence of water on Mars was obtained in 1872 by C. Vogel in 1872 by spectral analysis. This was disputed until the conclusive results of Adams in 1925 (also by spectral analysis).
Comet cores also contain water ice, and this was plausible since 19s century, by spectral analysis, but confirmed only in 1950s.
Jupiter's satellite Gannimede has oceans of frozen water, they probably contain more water that all oceans on the Earth, but this is a much more recent discovery which was made using spacecraft.
As I understand, the discovery of the liquid, flowing water was announced yesterday for the first time.
EDIT. The difficulty with finding water by spectral analysis is that some spectral lines come from the water vapor in the Earth atmosphere, when you observe from the Earth. So many of the early results until the middle of 20s century were questioned. In particular, Internet search does not give a clear reference for the first definite proof that comets contain water (ice). In any case this was widely believed in the first half of 20s century.
EDIT. Sometimes pieces of ice fall from the sky:-) The intriguing question whether they really come from meteorites (not from the Earth atmosphere) is discussed here: http://uregina.ca/~astro/Ice_Mets.pdf and here https://en.wikipedia.org/wiki/Megacryometeor