Why is money called "rhino"?

This is probably an unanswerable question, but an interesting suggestion is that the 'rhino' being alluded to is not the pachyderm, but the nose (as in rhinology or rhinoplasty), and 'rhino' as cash is linked to the earlier phrase 'paying through the nose'.

http://idioms.thefreedictionary.com/pay+through+the+nose

The hilarous A Classical Dictionary of the Vulgar Tongue (1785)

has these interesting entries:

RHINO, money, (cant)

RHINOCERICAL, rich (cant); the cull is rhinocerical

So these expressions might have been somewhat current in the late 1700:s

Other expressions for being rich:

GINGERBREAD:... also money; he has the gingerbread; he is rich

OAK a rich man, a man of good substance and credit

As you say, the origin is uncertain. The OED has mentioned the earliest instances of its usage, which are as follows:

1688  Shadwell, Sqr. Alsatia I:- "Thou shalt be rhinocerical, my Lad."

1699 Dunton's conversation in Ireland, Life & Errors (1818):- "It was pretty to see the Squire choused out of so fair an estate with so little ready rhino."

Brewer's Dictionary of Phrase and Fable suggests 'one plausible origin' as powdered rhino horn brought back from the East, commanding a high price for its reputed properties. Brewer's not good on definitive answers, but unbeatable for plausibility.