Mine works fine... just copied a bunch of stuff from my GoPro's SD card an hour ago, and I run iTunes using media on my SD card. Forgive me for asking, but did you go to Device Manager to see if your SD card reader was in/not in the list?
My SD Card reader works BUT 'Realtek USB 3.0 Card Reader', which I'm guessing is the SP3 built in SD card reader, continues high CPU usage when I close the cover and prevents the Surface going in to connected standby. My point there is that it seems like there's some issues with this driver and hopefully Realtek/Microsoft get this sorted out quickly.