Eldritch Blast is a Warlock cantrip, and Warlocks use their Charisma for their spells, even when you multiclass.
If I have Gale the Wizard (whose spellcasting stat is Intelligence) learn the Spell Sniper feat at level 4, which gives me a cantrip, and I choose Eldritch Blast even though I have no levels in Warlock, will Eldritch Blast use Gale's Intelligence, or his Charisma?
Baldurs Gate 3 – Which Stat Eldritch Blast Uses When Grabbing it from Spell Sniper Feat
baldurs-gate-3
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To skip the launcher in Baldur's Gate 3:
Right-click the game in the Steam game list and choose "Properties..."
Add the following in the "Launch Options" option in the "General" tab that opens:
--skip-launcher
Now hitting "play" in Steam will directly open the game, skipping the launcher.
Put simply, no.
Spell damage is calculated based on the dice shown on the spell - see this example from the Baldur's Gate wiki. A fireball will do 8d6 damage (increased based on upcasting) irrespective of the weapon you're holding.
(source: https://bg3.wiki/wiki/Fireball )
The dice you're looking at on a weapon relate strictly to the damage done with melee or ranged attacks with that weapon (and will be affected by strength / dexterity as with other weapons.) Some weapons, like the Mourning Frost, add additional melee damage, but this has no direct effect on spell damage. A spell is not a weapon attack and therefore has its own damage dice.
Notably, there are certain weapons that will have indirect effects on spells - such as the Spellsparkler which grants you lightning charges on a successful cast. In fact, the Mourning Frost you linked has a special effect that deals 1 additional cold damage, and this is triggered on the caster dealing cold damage by any means, and affects cold damage from any source, including a spell.
Best Answer
This is one instance where Baldur's Gate 3 differs from 5th edition.
The short answer is: the attribute used is whatever it says the attribute is when you're picking it.
For Gale, as a Wizard, this means INT. For any spellcasting class, it seems to use whatever your primary class' spellcasting ability is. (WIS for Clerics / Druids / Rangers, CHA for Bards / Warlocks / Paladins)
For anyone without spellcasting, it seems to use INT.