The ability that defines Smoldering Stagecoach's power works in all zones, not just the battlefield.

"Cascade" means "When you cast this spell, exile cards from the top of your library until you exile a nonland card whose mana value is less than this spell's mana value. You may cast that card without paying its mana cost if the resulting spell's mana value is less than this spell's mana value. Then put all cards exiled this way that weren't cast on the bottom of your library in a random order."

A spell's mana value is determined only by its mana cost. Ignore any alternative costs, additional costs, cost increases, or cost reductions.

Cascade triggers when you cast the spell, meaning that it resolves before that spell. If you end up casting the exiled card, it will go on the stack above the spell with cascade.

When the cascade ability resolves, you must exile cards. The only optional part of the ability is whether you cast the last card exiled.

If a spell with cascade is countered, the cascade ability will still resolve normally.

You exile the cards face up. All players will be able to see them.

If you cast a spell "without paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the spell has any mandatory additional costs, you must pay those to cast the card.

If the card has {X} in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.

Due to a 2021 rules change to cascade, not only do you stop exiling cards if you exile a nonland card with lesser mana value than the spell with cascade, but the resulting spell you cast must also have lesser mana value. Previously, in cases where a card's mana value differed from the resulting spell, such as with some modal double-faced cards or cards with an Adventure, you could cast a spell with a higher mana value than the exiled card.

The mana value of a split card is determined by the combined mana cost of its two halves. If cascade allows you to cast a split card, you may cast either half but not both halves.