Yeah, no need to use a Fate point, they get the benefit 'for free'. Note, however, that this isn't a guaranteed advantage, and can be a disadvantage. For example, if a war has flared up between Summer and Winter, a Winter Mark is going to look a lot like a bulls-eye to agents of Summer. The character will still get the +1 to social in such circumstances(particularly appropriate for intimidation).
Note that in cases where an NPC has reason to respect the mark, it might be reasonable to allow the player to spend Fate to invoke their High Concept (which would relate to the mark by definition) to get a further +2 on affected social rolls.