yeahbut.

long·horn (lông'hôrn', lŏng'-)
n.
1. Any of a breed of cattle with long horns, formerly bred in great numbers in the southwest United States.
2. A variety of Cheddar cheese molded into a long cylinder.

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The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2000 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.

So I don't reckon it does describe a breed as such, just a general description of type. After all, we used to have dairy shorthorn, beef shorthorn...

But I love the way that the second definition gives a further example of the migration of meaning via synecdoche (cow to cheese).