die Mähre
nag
An old, emaciated, or weak horse.
Der Bauer spannte die alte Mähre vor den Pflug.
The farmer hitched the old nag to the plow.

nag / hag
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nag
An old, emaciated, or weak horse.
Der Bauer spannte die alte Mähre vor den Pflug.
The farmer hitched the old nag to the plow.

'Mähre' (nag/hag) is an outdated word in both meanings. It is hardly used in modern everyday language and sounds archaic or literary.
In dem alten Roman ritt der Held auf einer müden Mähre.
In the old novel, the hero rode on a tired nag.
When the word refers to a woman, it is a very derogatory and strong insult. It should under no circumstances be used as a joke.
Er war so wütend, dass er sie eine böse Mähre nannte.
He was so angry that he called her an evil hag.
The meaning becomes clear from the context. If it is about animals, farms, or historical stories, it refers to the old horse. If the word appears as an insult in an argument, it has the insulting meaning for a woman.
Der alte Gaul war nur noch eine knochige Mähre.
The old horse was nothing but a bony nag.
horse
'das Pferd' and 'die Mähre' both refer to a horse, but they are not equally neutral. 'das Pferd' is the normal word for the animal, whether it is young, old, strong, or weak. 'die Mähre' means an old, thin, or weak horse and sounds derogatory. The words can be confused because a nag is also a horse. In normal conversation about riding, animals, or a farm, you almost always use 'Pferd'. 'Mähre' only fits when you want to emphasize the animal's poor condition.

Die alte Mähre zog den Wagen nur noch sehr langsam.
The old nag pulled the cart only very slowly.
Auf dem Bauernhof durfte Lena das Pferd füttern.
On the farm, Lena was allowed to feed the horse.