What should I do with the exposed grounding wire during a conversion from hardwired to plug in light fixture?
Lamp cord typically comes in 18/2, and 16/2 varieties. Neither of which has a grounding conductor. If the lamp... 


is intended to be used indoors 
will connect to the electrical system through a cord-and-plug attachment means
Does not have any exposed metal parts


you should be fine using a 2 wire attachment cord. However if the lamp...


will be used outdoors
will be hardwired
has exposed metal parts


then you should consider using an attachment cord with a grounding conductor, and connecting the grounding conductor to the grounding conductor in the fixture.