Traits

A straight, longer than average horn. 

A smooth, much shorter than average horn. SoftBots are born with nub horns, but it's very unusual for them to carry this trait into adulthood.

A small, straight horn. The most common horn length.

The horn shown to the side is the maximum length a small horn can be.

A straight, medium sized horn. The second most common horn length.

The length shown to the side is the maximum length for a medium length horn.

An extra long tube horn. Good for fanciful displays and showing off, but depending on the size it can really strain the neck. There's no definitive size limit, but don't make horns that go into orbit, please.

Royals, Nobles, and Guardians with extra long horns can magically retract them right down to being a nub, if they desire. Civilians and Nomads unfortunately lack this feature and must be very careful where they lay their head- but it's super rare for them to have extra long horns anyway.