Some cards have additional effects for each {S} spent to cast them. You can cast these spells even if you don’t spend any snow mana to cast them; their additional effects simply won’t do anything.

Snow isn’t a type of mana. If an effect says you may spend mana as though it were any type, you can’t pay for {S} using mana that wasn’t produced by a snow source.

If Search for Glory is copied, no snow mana was spent to cast the copy, so you won’t gain any life. You’ll still search . . . for glory.

A snow permanent card is any artifact, creature, enchantment, land, or planeswalker card with the supertype snow.

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.