Uruks/Ologs (Greenskins) were for the most part originally brought down into the Underdark as slaves and many remain slaves to this day. If you wish to play a greenskin, this could be as an individual within a house, whose exceptional talents have merited their inclusion in the party travelling to the surface gatherings or as a group, whose ancestors escaped their Drow masters and have managed to survive as a clan ever since.
Makeup Advice
Uruks/Ologs can be a very makeup intensive race, although many choose to use a mask. This limits makeup required and easily adds facial features.
If you are wishing to use make up it is worth noting that as of the latest version of the Rules (v4) the use of block black or brown makeup is not allowed within Lorien Trust events.
Playing Notes
Expect to be looked down upon by the Drow/Elves/Norns, but have your own pride, after all your abilities got you where you are now. Most Erdrejans have certain expectations of all things green and this may allow you certain leeway with behaviours that might not be tolerated from other races. Greenskins will generally wear rags, furs and leathers.