Spending more than one snow mana to cast Berg Strider won’t cause the artifact or creature to remain tapped for additional turns.

The enters-the-battlefield ability can target an artifact or creature an opponent controls that’s already tapped. If snow mana was spent to cast Berg Strider, the target won’t untap during its controller’s next untap step.

If Berg Strider enters the battlefield without being cast, no mana was spent to cast it. The enters-the-battlefield ability may still tap the target, but that permanent won’t be stopped from untapping during its controller’s next untap step.

Similarly, if an effect copies the creature spell that becomes Berg Strider, no mana was spent to cast the copy. The target won’t be stopped from untapping during its controller’s next untap step.

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.

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 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.

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.

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.