If either target is an illegal target as Blizzard Brawl tries to resolve, neither creature will fight and no damage will be dealt.

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.

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.

You can’t cast Blizzard Brawl unless you choose both a creature you control and one you don’t control as targets.

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.

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

Check whether you control three or more snow permanents as Blizzard Brawl is resolving to see if the target creature you control gets +1/+0 and gains indestructible. That creature will still fight even if it doesn’t get those bonuses.

If the creature you control is still a legal target as Blizzard Brawl tries to resolve but the target creature you don’t control isn’t, the creature you control will still get the bonuses until end of turn.