When is the effect replaced with doubling season, on casting or on resolution? If doubling season is destroyed in response to my summoning a planeswalker for example, is the effect that created the counters locked in at double when the planeswalker was cast?

On resolution, so you won't get double counters.

Replacement effects have to exist just before an event is about to happen for them to replace that event. The event that's being replaced here is “the planeswalker spell card enters the battlefield with loyalty counters equal to its printed loyalty.” As you cast a planeswalker, the game doesn't know that it's ever going to enter the battlefield, let alone how many counters with.

Daniel Kitachewsky
L3, Paris, France
Rules NetRep