Do wolves prevent hostile mobs from spawning?

Solution 1:

No they do not.

Wolves spawn and are tamed as passive mobs (I'm unsure whether this means that they will prevent new passive mobs from spawning).

Hostile and passive mobs have a diffrent mob cap. They do not share this cap.

The only time that a wolf will help prevent hostile mobs from spawning, is if you attack it while it's not tamed, so that it becomes hostile, at which point it will join the hostile mob cap list and will behave like hostile mobs (despawning etc.)