I've seen a number of users with a similar problem - My Open with Explorer button is greyed out on my SP 2013 libraries. A lot of users pointed to it being an 64bit IE problem, but that's not the case for me. The Connect to Outlook and Export to Excel features work. It appears to be for all document libraries I have in my site collection. Is there a feature I need to switch on to enable this functionality or something else I'm missing?