Costs happen before effects.
Therefore when
PAthS is played, one burden is added.
-This causes the text of
Easterling Polearm to kick in (bearer cannot take wounds)
Then you wound every minion skirmishing the ringbearer.
-However this doesn't happen due to the polearm's text.
I hope that's clear. Another example is
Black Rider exerting to play
Relentless Charge with no other wounded minions and
Rumil, Silvan Elf in play.
You exert the
Black Rider as the cost before the effect is calculated. This causes Rumil to become an archer as you can now spot a wounded minion.
Then the effect is calculated, so Rumil gets wounded along with every other archer companion.