Green’s Dictionary of Slang

softhorn n.

1. a donkey, an ass.

1890–1904

Farmer & Henley Sl. and Its Analogues.

2. a simpleton, a fool.

1836		T. Haliburton Clockmaker I 269: I allot [...] that the blue-noses are the most gullible folks on the face of the airth — rigular soft horns, that’s a fact.
1840		T. Haliburton Clockmaker III 58: He thinks he has a soft horn to deal with.
1859		Hotten Dict. of Modern Sl. etc.
1864, 1867, 1870		Hotten Sl. Dict.
1873		Sl. Dict.

In phrases

soft is your horn [Bee cites a supposed Irishman who mistook a jackass – with its soft ears – for a bull – with hard horns]

you’re mistaken, lit. ‘you’re an ass’.

1823

‘Jon Bee’ Dict. of the Turf, the Ring, the Chase, etc.