Well there's good news and bad news:
The good news is that Arnie really DOES have a collection of about 25 luxury Swiss wrist watches!
The bad news (for your meme) is that his watches are made by Audemars-Piguet, including every Royal Oak variation used in his TERMINATOR movies. If your local library has back-issues of WatchTime Magazine, his interview is in the
November/December 2012 issue.