Dreadhorde Arcanist — ruling 1

The instant or sorcery card you target must have mana value less than or equal to Dreadhorde Arcanist's power immediately after Dreadhorde Arcanist has attacked. Any other abilities that trigger when creatures you control attack won't have resolved yet.

Dreadhorde Arcanist — ruling 2

If Dreadhorde Arcanist leaves the battlefield before its triggered ability resolves, use its power as it last existed on the battlefield to check whether the card is still a legal target.

Dreadhorde Arcanist — ruling 3

If you cast the card, you do so as part of the resolution of Dreadhorde Arcanist's triggered ability. You can't wait to cast it later in the turn. Timing permissions based on a card's type are ignored, and the spell will resolve before blockers are declared.

Dreadhorde Arcanist — ruling 4

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

Dreadhorde Arcanist — ruling 5

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.

Dreadhorde Arcanist : règles, fonctionnement et interactions (MTG)

Dreadhorde Arcanist is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Trample Whenever this creature attacks, you may cast target instant or sorcery card with mana value less than or equal to this creature's power from your graveyard without paying its mana cost. If that spell would be put into your graveyard, exile it instead.

How it works : Dreadhorde Arcanist

Original English text — Wizards of the Coast / Scryfall

#1March 19, 2021· Wizards of the Coast
The instant or sorcery card you target must have mana value less than or equal to Dreadhorde Arcanist's power immediately after Dreadhorde Arcanist has attacked. Any other abilities that trigger when creatures you control attack won't have resolved yet.
No other card is named in this ruling.
#2March 19, 2021· Wizards of the Coast
If Dreadhorde Arcanist leaves the battlefield before its triggered ability resolves, use its power as it last existed on the battlefield to check whether the card is still a legal target.
No other card is named in this ruling.
#3March 19, 2021· Wizards of the Coast
If you cast the card, you do so as part of the resolution of Dreadhorde Arcanist's triggered ability. You can't wait to cast it later in the turn. Timing permissions based on a card's type are ignored, and the spell will resolve before blockers are declared.
No other card is named in this ruling.
#4March 19, 2021· Wizards of the Coast
If you cast a card "without paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, you must pay those to cast the card.
No other card is named in this ruling.
#5March 19, 2021· Wizards of the Coast
If the card has in its mana cost, you must choose 0 as the value of X when casting it without paying its mana cost.
No other card is named in this ruling.