Following up on
Does Improved Divine Smite trigger when a paladin makes an unarmed strike?

Improved Divine Smite will not trigger on an unarmed strike.

Context

The paladin in my campaign – covered in my previous question – is a minotaur. This means he could attack with his horns, to potentially trigger Improved Divine Smite.

Minotaur, Unearthed Arcana: Centaurs and Minotaurs:

Horns. Your horns are natural melee weapons, with which you’re proficient. When you hit with
them, the target takes piercing damage equal to 1d6 + your Strength modifier.

Paladin, PHB page 85:

Improved Divine Smite. By 11th level, whenever you hit a creature with a melee weapon, the creature takes an extra 1d8 radiant damage.

Question

Do natural melee weapons from racial traits trigger Improved Divine Smite?

In other words, do natural weapons count as melee weapons? Or is there some other rule that categorizes/treats natural melee weapons differently from other melee weapons?

For my campaign I'm mostly interested in the natural melee weapon from minotaurs. I'm assuming, however, the same rules would apply for other natural melee weapons gained through racial traits – e.g. a lizardfolk's Bite, tabaxi's Claw, centaur's Hoove, etc. If this assumption is wrong, please enlighten me.

Yes, if the racial rule calls them weapons

As your other linked answer states, Unarmed Strikes do not work for Improved Divine Strike because the rules say Unarmed Strikes are not weapons:

Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons).

But the racial ability for Minotaur horns specifically says the horns are a weapon:

Your horns are natural melee weapons

What is happening here is that there is a specific rule/allowance for the Minotaur that is similar to (but different from) a general prohibition.

The minotaur is not making an Unarmed Strike (a head-butt). It is making an attack with a weapon which happens to be located on its head.

Contrast this with the Aarakocra's Talons:

Talons

You are proficient with your unarmed strikes, which deal 1d4 slashing damage on a hit.

(Hat tip to Justin)

Yes, if it says they are weapons

The Minotaur race Horns racial feature says (emphasis mine):

Your horns are natural melee weapons, with which you’re
proficient. When you hit with them, the target takes piercing damage
equal to 1d6 + your Strength modifier.

Divine smite says:

By 11th level, whenever you hit a creature with a melee weapon, the creature takes

an extra 1d8 radiant damage.

So, in this case it is valid, as it says that your horns are weapons. However, this only applies to the Minotaur race. Racial attack abilities vary between races. For instance, the Aarakockra race's Talon racial feature says:

You are proficient with your unarmed strikes, which deal 1d4 slashing damage on a hit.

In this case, it does not say that the talons are weapons, and it therefore follows the 'it does not work' unarmed strikes path.

You can tell the difference between the racial attacks eligible for Improved Divine Smite, and those ineligible, as the valid ones say that it is a weapon, and the not valid ones don't.