Does a subpanel ground need to be insulated wire
No insulation is required.  However grounding to a rod is not enough, you must also run a ground wire back to the supply. 

Dirt is a poor conductor and you can't expect it to return the 100 amps + that it must to assure a breaker trip during a ground fault.  When it can't, it will not trip and leave a condition where all your grounds are energized at line voltage.