He claims that this is within A Winter's Tail, Act I, Scene ii - in the first folio.

So, I turned to the First Folio viewer which allows people to see scans of the first printing of The Winter's Tale - in this case, the New South Wales scan. Direct link to scan.

The "emoticon" is also present in the second folio, the third, and the fourth.

However, at some point, the smiley vanishes!

The fourth folio was printed in 1685. By 1786, the :) had dropped out - as seen in this British Library edition by John Bell. (The annotations to the 1786 edition make no mention of any changes to the particular soliloquy.) In just 100 years, some form of mutated Grammasites must have eaten up the parentheses.

Google Books is a fine resource - but, as far as I can tell, it doesn't allow one to search a particular time period.

Thanks to Imran Ghory for telling me about Copac - an electronic resource to search British academic libraries. So, by crafting a specific query, we can see all the publications within a specific timeframe.

Sadly, most of the resources are locked behind the Athens system. An academic system managed by Eduserv.

OpenAthens says it is:

Unlocking the door to knowledge

Ah, yes, the famous "Unlocking knowledge by locking away behind paywalls" strategy. We all know how well that works out...

So, the hunt is on! If you have access to these long-out-of-copyright resources, perhaps you can discover when the original smiley was exorcized and who was responsible for it?