Natural weapons aren't (intended to be) treated as weapons
Official 5e rules designer Jeremy Crawford clearly addresses whether natural weapons are "weapons" here:
Interesting point in Dragon Talk today, you mentioned the "natural melee weapon" language of the minotaur's horns means it works with Divine Smite (and magic weapon?). That seems at odds with previous answers regarding bite attacks. Is this a revision?
Or are PC minotaur horns/centaur hooves somehow mechanically different from a monster minotaur's horns/monster centaur's hooves?
I'll boil it down for you. When we wrote the "Player's Handbook," we meant the weapons on the weapon table when we wrote "weapon," unless we said otherwise. But you break nothing in the game if you let natural weapons go along for the ride.
...So they have no such weapon properties
Crawford responds to a since-deleted tweet about the properties of natural weapons here:
Are natural weapons considered finesse weapons? A lot of them use dex for to-hit and damage, but I can't find a reference.
No. A weapon has the finesse property only if its description says so, and using Dex. to hit doesn't equal finesse.
By virtue of not being weapons, natural weapons also don't have the properties that actual weapons do, unless explicitly stated otherwise.
But attacks with natural weapons are generally still melee weapon attacks
The user Crawford responds to in that first conversation also references a tweet in this conversation with Crawford by some others:
Does the magic weapon spell work on natural weapons (thinking about beast master rangers specifically)?
The magic weapon spell targets weapons (PH 146–49), not body parts. A DM can rule otherwise and not break it.
wait! this would undo every fighter / druid. beast natural atks are melee weapon attacks (q.v.)
See the druid's Primal Strike feature.
yes, of course, but any precedent that says beast natural is not a weapon has breaking reach.
Their attacks count as weapon attacks, but the system doesn't consider their body parts weapons.
wouldn't that mean every ftr type / drd multiclass is undone, unable 2 use 'weapon' abilities?
Many fighter abilities rely on a weapon attack or a melee attack. Natural weapons qualify for both.
ok. I'm still confused on when a natural weapon is considered a weapon by the rules & when not.
Most of the system only cares whether an attack is a weapon attack, not whether the thing used is a weapon.
As Crawford says, they're not technically classed as actual weapons, but they're still usually used to make melee weapon attacks - just as unarmed strikes are - and most related class features trigger off weapon attacks or specifically melee weapon attacks rather than requiring a weapon or relying on the weapon's properties. (The rogue's Sneak Attack is a notable exception, requiring a finesse or ranged weapon.)
(And as clarified here, natural weapons are not used to make unarmed strikes unless something explicitly states otherwise - most features giving natural weapons to player races do specify that the natural weapon can be used for unarmed strikes.)