Strange English mnemonic: 'S' before 'N', except after the 15th century

As Third Idiot noted, some of these “s before n” come from a Old French, along with a lot of cases of “s before other consonants”. Most of them came from Latin, either directly (sperare gave espoir [hope], hospes, hospit- gave hospital, testa gave teste [head]), others by contraction (asinus gave asne [donkey]) or deformation (fraxinus gave fresne [ash tree]). As an example of a word with close history to the one you're enquiring about, puisne (a legal term) comes from Old French puisné, from Latin roots post [after] and natus [born]. The French word is now written puîné, and I'll describe this process below.

There was later a movement of suppression of the s before many other consonants, starting in the 12th century and going all the way to the 17th. The s was dropped, but remained in pronunciation and was marked with a circumflex accent: asne became âne (pronounced /ɑn/), with the accent a sign that it is not to be pronounced /an/. Other examples above: hospital became hôpital, teste became tête, fresne became frêne, etc. The process wasn't exhaustive, as words with less usage (or scientific words) kept their s: e.g. the adjective hospitalier (cf. the noun hospital).

While this has been a long digression into French, it seems to confirm that people with knowledge of Old French at the time would be inclined to include s before other consonants, though I cannot figure out why n is singled out in the paragraph you quote.

Edit: NateMPLS cites rein, which I hadn't thought about. It comes from Old French rene (Modern French would be rêne), from earlier French resne, from Latin retina. It doesn't have the s in English because it was borrowed from French after the s was dropped.

Words that may have arised:

See the entry for "Rein" (Google books, Imperial Dictionary of the English Language)

There are plenty of words where 's' is behind 'n'.

Snake
Snowfall

Or if you desire something else:

Mesne (Definition: Intermediate or intervening; median) Visne (Definition: vicinity.) Esne (Definition: Member of the lowest class; This is Old English) Puisne (Definition: In law, a subordinate)

The next word I am about to give you may answer your second question:

Fresne

This is actually a French word. You can probably draw the connection between popularity of words with 'sn' and the close association of the French language with the English language in the 15th century.

http://dictionary.reference.com/