Is the HD an NTFS or FAT32 format? I don't have a Nexus10 but my Nexus7 can't read NTFS drives.
It could be this, but also how does your portable HD get power? If it normally is powered via USB when connected to a computer, that could be a problem, as I don't believe the N10 using the OTG cable supplies full power to devices connected to it, so it may need an external power source? Again, I don't know for sure, just throwing that out there.
Formatting could also be an issue. Most folks use OTA with smaller devices, such as USB flash drives, which are usually formatted as FAT. A larger drive formatted for Windows (NTFS) will probably not be recognized, as zedora mentioned.