I googled that a few years back and found this;
Method #1: If you have a hex editor, you can look at the file header. At byte offset 240 (0xF0) there'll be either "PE..d" (indicating 64-bit) or "PE..L" (indicates 32-bit). Works for dlls and executables. Don't know about other binaries such as drivers, though.
Method #2: Use a file-info tool such as the free Filealyzer (PE Header tab). This one's useful for other file types, too, even MP3s.