Can I use critical hits under the effect of "Greenskins Invade"?
When one rolls a 6, the die isn't technically re-rolled. According to the rulebook, the rolling a 6 causes an additional die to be rolled.


  In addition, every result of 6 EXPLODES, which means that the attacker rolls one additional battle die immediately (which causes an additional hit on a 4, 5, or 6, and which explodes again on a 6).


Which makes it clear that if the Old World card limits my dice to one, then I wouldn't be able to roll an additional die even if it would explode.