Can plastic planters be 'aged' in the same way that clay/terracotta pots can with yogurt, beer, moss etc? Answered

First thing that comes to mind is to wash it with TSP (to prepare for paint) and then fake the aged effect with outdoor paints. I'm a terrible painter so I'll leave that one open, but an amature decorator can do a lot with paints. If you want to just remove the shine, get a piece of fine sandpaper and scratch it up. Consider scratching only in one direction, in circles, in cross-hatches, or some other design. If you scuff it up with a coarse sandpaper, you might create a surface that moss can adhere to. That might even be worth trying, but if it doesn't work your pot is probably ruined.

Clay pots are really happy to grow all sorts of lichens and algae/moss. This is because they are porous and hold nutrients and water, as well as provide a surface for the little guys to grow on. I can't say from experience, but try roughing up the surface as fox says, then apply all sorts of moss-food. worst case scenario you'll have a dirty pot. Perhaps sew a burlap 'cone' the shape of the outside of the pot, then attaching that with hot glue. It's porrous, and should be happy to grow moss.