Search for Glory

The {S} symbol is a generic mana symbol. It represents a cost that can be paid by one mana that was produced by a snow source. That mana can be any color or colorless.

Snow is a supertype, not a card type. It has no rules meaning or function by itself, but spells and abilities may refer to it.

If you cast Search for Glory without spending snow mana, you won’t gain any life. You’ll still perform the search.

The Kaldheim set doesn’t have any cards with mana costs that include {S}, but some previous sets do. If an effect says such a spell costs {1} less to cast, that reduction doesn’t apply to any {S} costs. This is also true for activated abilities that include {S} in their activation costs and effects that reduce those costs.