So, yesterday I talked about why somebody might cut off a horse's tail, but what about the mane?
Some breeds are traditionally turned out with a "full" mane. This includes the Arabian and all of the British "native" pony breeds.
This Icelandic mare has a full mane, correct for her breed. Horses kept in cold climates also benefit from having a full mane. It keeps their ears warm! (Literally - the ears are pulse points - if they're cold, the horse feels cold).
Most horses have their manes shortened. The length varies. Stock horses, for example, usually have shorter manes than Thoroughbreds and sport horses. The mane is not shortened by cutting it (which makes it bushy) but by pulling out the long hairs using a comb.
This Paint/Draft cross has a medium length mane. Stock horse breeders generally trim to about half this length.
Finally, in some cases, the mane may be shaved off completely. This is called hogging in the UK and roaching in the US.
Hogging or roaching is traditional for English hunting cobs, Norwegian Fjords, and mules (In the last case, mules tend to grow very sparse manes). An owner may also roach the mane for temperature control, such as if keeping ponies in very hot climates, or pure aesthetics. The forelock may be left on or may also be clipped (Some people believe that leaving the forelock on helps keeps flies away from the horse's eyes).
These saddle mules have had their manes roached completely, including the forelock - again, mules tend to grow very sparse manes and generally look better "shaved."
In slight contrast, this Norwegian Fjord mare has had her mane roached and then allowed to grow out partially - giving her a "manehawk." This is traditional and correct for the breed and is done to show off the two-toned mane that's a breed characteristic. The forelock has been left long.
So, all kinds of different "mane-dos." For worldbuilding, traditions in mane length could be used to demonstrate different cultures. (For example, real-world Romany tend not to trim or shorten the manes of their horses).