What is the origin of idiom wrap someone in cotton wool?

This extract from the 1848 publication 'Letters of Mrs Adams' [Abigail Adams; via Google Books]

... I expected to have seen a rough, stout, warlike , Roman,– instead of what I should sooner think of wrapping him up in cotton wool, and putting him into my pocket, than sending him to contend with cannon-balls.

seems an early example showing the development of the metaphorical usage.

Though the metaphor is transparent, it's instructive to see how the final form of a metaphor might arise, stepwise.

A Dictionary of Slang and Unconventional English by Eric Partridge defines the expression

Wrap (keep) in cotton wool: cosset, cuddle. Colloquial, from ca. 1870, by mid. 20 c. almost Standard English.

It may not be the answer but I believe it is useful.

I found an 1832 publication "Ackermann's Juvenile Forget Me Not" which uses the same idiom, although it is more of a wrap something up in cotton wool than wrap someone up in cotton wool. The relevant portion is quoted below Ackermann's Juvenile Forget Me Not [R. Ackermann; via Google Books]:

"O! don't touch, don't touch one thing, Sophia dear! This is the beautiful little vinaigrette which you gave me, and which you see I always keep wrapped up in cotton wool.

This seems an earlier example than the example in Edwin's answer.