Ability to cast for overload cost or just cast

Question

Dreadhorde Arcanist allows you to "cast target instant or sorcery card with converted mana cost equal to or less than dreadhorde arcanists power from your graveyard without paying its mana cost" but for cards with overload costs that state in it's own separate ruling that we "may" cast it for its overload cost, can I use dreadhorde archanist to reach and have the ability to cast a card like "weapon surge", then choose to pay its overload cost for its overload effect?

Answer 1

No, you cannot pay the overload cost for spells cast that way.

Dreadhorde Arcanist allows you to cast a spell with an alternate cost of "without paying its mana cost", as described in rule 118.9:

Some spells have alternative costs. An alternative cost is a cost listed in a spell's text, or applied to it from another effect, that its controller may pay rather than paying the spell's mana cost. Alternative costs are usually phrased, "You may [action] rather than pay [this object's] mana cost," or "You may cast [this object] without paying its mana cost." Note that some alternative costs are listed in keywords; see rule 702.

The Overload ability also defines an alternate cost in rule 702.95a:

Overload is a keyword that represents two static abilities that function while the spell with overload is on the stack. Overload [cost] means "You may choose to pay [cost] rather than pay this spell's mana cost" and "If you chose to pay this spell's overload cost, change its text by replacing all instances of the word 'target' with the word 'each.'" Using the overload ability follows the rules for paying alternative costs in rules 601.2b and 601.2f-h.

Then rule 118.9a says this:

Only one alternative cost can be applied to any one spell as it's being cast. The controller of the spell announces their intentions to pay that cost as described in rule 601.2b.

Since Dreadhorde Arcanist's effect specifically allows you to cast the spell with its alternate cost, you cannot choose to pay the overload cost.

Answer 2

I believe that a player has the right to choose an instant or sorcery card with overload, and to play it through his overloaded ability too.
This is also because Gatherer's rulings on Weapon Surge card explicity say that (15/4/2013):

• "Casting a spell with overload doesn’t change that spell’s mana cost. You just pay the overload cost instead".

The fact that the overload cost is reduced to zero means nothing.
The Gatherer's rulings that say:

"If you are instructed to cast a spell with overload "without paying its mana cost", you can't choose to pay its overload cost instead"

it only means that,if the player,for some strange reason,want to pay the mana, would not however: he cannot choose to pay the mana indicated by the overload ability even if he wanted to.
But it doesn't mean that the overload ability can't be played for this reason.
Thus, since Dreadhorde Arcanist has a power equal to 1, and Weapon Surge converted mana cost is 1 too, then everything is ok, and it would seem that the answer to this question could be:- "Yes" .

(In fact, my first answer to this question was just that. The following is not all flour of my bag, but is rather due to the inspiration followed by the vision of the excellent response of Murgatroid99, to which I refer).

But it is now important to say that:

Only one alternative cost can be applied to any one spell as it's being cast. The controller of the spell announces their intentions to pay that cost as described in rule 601.2b.

Thus, it is for this reason that the answer to this question cannot be positive.
Since you are already forced to pay an alternative cost (that is "without paying its mana cost"), you cannot choose to pay for a different one.
In other words,you cannot pay the overload cost,since it is a kind of alternative cost.