I think the answer may have more to do with the meaning of the English word "green" than with the Hebrew.
Meaning of the word "green" in English and Hebrew
One of the two dozen or so definitions of the adjective "green" given by the Complete Oxford English Dictionary (A.I.2) is "covered with a growth of herbage or foliage" - a mode of the word that, according to the OED, dates back to the time of the Saxons. Another definition of the word (A.I.5) is:
(a) Unripe, immature; (b) young and tender; (c) full of vigourous life, flourishing; (d) retaining the natural moisture, not dried.
This meaning also dates back to Saxon times.
Apparently the same sense of the word was present in medieval Hebrew. The Talmudic scholar Rashi (1040-1105) comments on the verse (in English translation):
In grassy pastures. Since he commences to compare his sustenance to
the pasture of an animal by saying, “The Lord is my shepherd”, “green
pastures” is appropriate for the expression.
Early English translations of Psalm 23:2
The earliest English translation of the Psalm from Hebrew using the word "green" I could find was Tyndale's translation of the Psalm, dating to around 1526:
The Lord is my shepherde, I can wante nothinge. He fedeth me in a grene pasture ...
Coverdale's translation was completed around 1535 and reads:
The Lorde is my shepherde, I can wante nothinge. He fedeth me in a grene pasture ...
The Geneva Bible (c. 1560) follows the same convention, as does the 1537 "Matthew's Bible" and the Whitchurch "Great Bible" of 1539, though these latter two were not strictly a translation of the Hebrew.
The Lord is my shepherd, I shal not want. He maketh me to rest in grene pasture ...
Curiously though, the Bishop's Bible, dating back to 1568 and then the official Bible of the Church of England, uses a phrase that is closer to the literal Hebrew:
God is my sheephearde, therfore I can lacke nothyng he wyll cause me
to repose my selfe in pasture full of grasse ...
King James Version
Instruction #14 to the translators of the King James Bible commanded:
These translations to be used when they agree better with the text
than the Bishops’ Bible: Tyndale’s, Matthew’s, Coverdale’s,
Instruction #1 is even starker:
The ordinary Bible read in the church, commonly called the Bishops’
Bible, to be followed, and as little altered as the truth of the
original will permit.2
In the case of Psalm 23, though, they decided to use what Tyndale and others had indicated, rather than the Bishop's Bible, even though the Bishop's Bible "agreed better with the text":
The Lord is my shepheard, I shall not want. He maketh me to lie downe in greene pastures ...
This may be in part due to the desire of the translators to provide somewhat of a balance between style and literacy where possible. In his book Bible: The Story of the King James Version, Gordon Campbell, Professor of Renaissance Studies at the University of Leicester, writes:
The balance between the public reading and private study of the Bible
has shifted over the centuries with the rise in literacy. In the
seventeenth century the Bible was more often heard than read, and it
is clear that the translators had the practice of reading aloud (in
homes as well as churches) in mind. Part of the evidence for this is
punctuation, which tends to be rhetorical rather than grammatical, but
the clearest manifestation of the emphasis on the need to provide a
text that can be read aloud is the rhythms of the KJV. The text is
prose, but it often has the pulse of poetry. Adam, blaming Eve for the
fall, says ‘she gave me of the tree, and I did eat’ (Genesis 3:12), a
perfect iambic pentameter line (and one that Milton incorporated
intact into Paradise Lost); in the next verse, God says to Eve ‘what
is this that thou hast done?’ (Genesis 3:13), a perfect iambic
tetrameter line. The seventeen words that I have quoted are all
monosyllables cast in prose, but their regular rhythm makes them easy
to read aloud.3
A possible answer to the question given the above
So to summarize a possible answer to your question, "Why is 'pastures of grass' translated to 'green pastures' (or similar)," I think one could say (a) because that is how it has been translated from Hebrew since at least 1526 in other respected English translations (including the King James), and (b) because the full meaning of the English word "green" seems to support the translation,3 as warranted by the Oxford English Dictionary and at least one Talmudic commentator.
Excursus: Some still earlier English translations
The next earliest translation to Tyndale's - I believe Wycliffe's Bible (c. 1390) - uses a different phrase:
The Lord gouerneth me, and no thing to me shal lacke; in the place of leswe ...
where leswe is a Saxon word meaning "pasture". The ancient Vespasian Psalter, dating to the 8th century, uses the phrase stowe leswe, where stowe is another archaic word meaning place (a discussion of the phrase can be found here). Both Wycliffe and the Vespasian Psalter, however, are translations of the Latin Vulgate and not out of Hebrew. The Vulgate reads:
Dominus regit me, et nihil mihi deerit: in loco pascuæ, ibi me collocavit.
In the case of the Psalms, the Vulgate translates the Septuagint, which contains the phrase τόπος χλόης (topos chloēs), meaning "place of the first shoots (of plants)" or "tender grass". Brenton's translation of the Septuagint (1844) chose to use the phrase "place of green grass", departing also from the strictly literal Greek.
1. Bible: The Story of the King James Version (Oxford University Press, 2010), p.39
2. Ibid., p.35
3. Ibid., p.80
4. It seems to me that in considering translation alternatives, the scope of the word to be translated is considered fairly fully, but the scope of potential target words in English is not. An example of this would be the use of the word "atonement". Up until after the King James Version was published, the English word "atonement" meant reconciliation and had no connection with recompense or punishment. Modern translators have retained the use of the word "atonement" in the negative sense, not realizing perhaps that when the word was originally chosen it didn't have the same meaning they now impute to it.