Question: Which kinds of non-competitive reacreational riding activities can horses perform?
About the article "Equestrianism", section "Overview of equestrian activities".

Candidate passages:
Horses are trained and ridden for practical working purposes such as in police work or for controlling herd animals on a ranch.
They are also used in competitive sports including, but not limited to, dressage, endurance riding, eventing, reining, show jumping, tent pegging, vaulting, polo, horse racing, driving, and rodeo.
(See additional equestrian sports listed later in this article for more examples.)
Some popular forms of competition are grouped together at horse shows, where horses perform in a wide variety of disciplines.
Horses (and other equids such as mules and donkeys) are used for non-competitive recreational riding such as fox hunting, trail riding or hacking.
There is public access to horse trails in almost every part of the world; many parks, ranches, and public stables offer both guided and independent riding.
Horses are also used for therapeutic purposes, both in specialized paraequestrian competition as well as non-competitive riding to improve human health and emotional development.
Horses are also driven in harness racing, at horse shows and in other types of exhibition, historical reenactment or ceremony, often pulling carriages.
In some parts of the world, they are still used for practical purposes such as farming.
Horses continue to be used in public service: in traditional ceremonies (parades, funerals), police and volunteer mounted patrols, and for mounted search and rescue.
 A horse with a dished face or dished head has a muzzle with a concave profile on top, often further emphasized by slight bulging of forehead ("jibbah").
Dished heads are associated with Arabians and Arabian-influenced breeds, which excel at Endurance riding and were originally bred in the arid Arabian desert.
There are several theories regarding the adaptive role of the dished head.
It may be an adaptation to reduce airflow resistance and increase aerobic endurance.
Dished head is not considered a deformity.
A Roman nose is a muzzle with a convex profile.
Convex heads are associated with Draft horses, Baroque horse breeds and horses from cold regions.
This trait likely plays a role in warming air as it is inhaled, but may also influence aerobic capacity.
Roman nose is not considered a deformity.
A horse with small nostrils or small nares can be found in any breed and often accompanies a narrow jaw and muzzle.
Small nostrils limit the horse's ability to breathe hard while exerting itself.
This especially affects horses in high-speed activities (polo, racing, eventing, steeplechase) or those that need to sustain effort over long duration (endurance, competitive trial, combined driving).
Horses with small nostrils are therefore best used for pleasure riding or non-speed sports.  
 horses.
All riding horses can benefit from use of dressage principles and training techniques.
However, horse breeds most often seen at the Olympics and other international FEI competitions are in the warmblood category.
Many other breeds are seen at various levels of competition.
In non-competitive performances of classical dressage that involve the "Airs above the ground" ("described below"), the "Baroque" breeds of horses, most notably the Lipizzaner, are seen most often. 
Natural hoof care is the practice of keeping horses so that their hooves are worn down naturally and so do not suffer overgrowth, splitting and other disorders.
Horseshoes are not used but domesticated horses may still require trimming, exercise and other measures to maintain a natural shape and degree of wear.
Within the natural hoof care philosophy, the term barefoot horses refers to horses which are kept barefoot full-time, as opposed to horses who are fitted with horseshoes.
The hooves of barefoot horses are trimmed with special consideration to a barefoot lifestyle.
The barefoot horse movement advocates a generalized use of barefoot horses, both in non-competitive and competitive riding, often coupled with a more natural approach to horse care.
Horses are kept barefoot in many parts of the world, including South America, Mongolia and other industrialized and non-industrialized cultures. 
Equestrianism (from Latin equester, equestr-, "horseman", "horse") more often known as riding, horseback riding (American English) or horse riding (British English) referring to the skill of riding, driving, steeplechasing or vaulting with horses.
This broad description includes the use of horses for practical working purposes, transportation, recreational activities, artistic or cultural exercises, and competitive sport.