Will a hexed creature that is affected by splash damage (e.g. the green-flame blade spell from the Sword Coast Adventurer's Guide) take hex damage as well?
"Splash damage" doesn't have any special definition in D&D 5e, so I assume you're using it to refer to "damage taken by players or objects in the area surrounding a point of [...] impact".
Hex only does damage when you hit the target with an attack.
From the description of the hex spell:
Until the spell ends, you deal an extra 1d6 necrotic damage to the target whenever you hit it with an attack.
Green-flame blade's additional damage is not an attack.
See the spell description of green-flame blade (SCAG p. 143):
As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell’s range, otherwise the spell fails. On a hit, the target suffers the attack’s normal effects, and green fire leaps from the target to a different creature of your choice that you can see within 5 feet of it. The second creature takes fire damage equal to your spellcasting ability modifier.
The original melee weapon attack against the first creature specified by green-flame blade is, of course, an attack. However, the additional damage that the spell deals to a different creature within 5 feet is simply automatically dealt; there is no attack that can hit or miss.
A hit is when you make an attack roll and succeed. A miss is when you make an attack roll and fail.
The only things that are attacks are things with attack rolls, or things that are specifically stated as such (e.g. a shove or a grapple is described as a "special melee attack"). For more details, see this question: What counts as an attack?
As such, the "splash damage" of green-flame blade in particular does not meet the necessary condition for the extra damage from hex. For other causes of "splash damage", it depends on whether an attack roll is being made (and whether that attack roll hits, of course).