I have an S3 with 16 gigs and an additional 16 gigs of storage on an SD Card.
There is definitely some odd issues with SD Cards. Mine was recognized by the Phone and all applications up until about a week ago. I was able to listen to music using Music Player and Music Hub with no issues what so ever. Also, exported playlists out of iTunes and into the Music Folder on the SD Card. Playlists played with no issues there, either.
Not sure what odd ball event occurred, but none of the Music Players see the SD Card except Sound Player. That is, I see the SD card from the phone (Settings -> Storage) and can view the contents (music files and movies) using "My Files". However, Music Player, Music Hub, and Google Music do not see any of the music in the /storage/extSdCard/Music directory.
I have tried reformatting the SD Card and re-transferring the music, but still those apps will not see the SD Card (again the OS and the "My Files" app do see it).
I gave up on those music applications after wasting many frustrating hours combing through posts like this.
My work around was as follows:
After the Music Players mentioned above are suddenly no longer able to see the music on the SD Card, I tried a few other Music Players.
The only one that seemed to work is ProAmp. It allows the user to select the location of the music files, which included the SD Card.
I put sub-directories under the "Music Folder" named after my playlists, and dropping music from each playlist into each folder. By the way, ProAmp will also easily allow you to create Playlists as well, but a directory based playlist structure seemed easier.
By the way, I transfer music like others have mentioned....
Attached the S3 to my Windows Desktop via USB. It was recognized immediately. I created a folder on the SD card called Music, then transferred a few hundred songs by selecting all songs in my favorite playlist in iTunes to a folder on my desktop, then transferring those folders/songs to the Music Folder on the SD Card.
ProAmp was $3.99.