We have had users report the inability to open a document library item in SharePoint 2007 using the "Actions" -> "Open with Windows Explorer" option. We use Windows 7 OS and Office 2010.
You have to use 32-bit Internet Explorer to get this option to work correctly. The reason, as I understand it, is that it relies on ActiveX controls that are not available in 64-bit flavors.
If you go to the start menu and type 'internet explorer' in the bottom text box, you should see 2 shortcuts. One of them says "Internet Explorer (64-bit)". Make sure you do not use this one to launch IE.
Adding site to IE 11 trusted sites list made the "Open with Explorer" control visible (SharePoint 2010, Windows 7, IE 11 32 bit)