Wendy,
Yes to all of the above regarding mane. Mane orientation can depend on several factors.
Breed- Some horses have heavier manes than others. This also includes mane length. These factors can be genetic, environmental and diet.The result is a longer mane or heavier haired mane may part in the center. Where as a shorter mane or thinner hair may go to one side or the other.
Grooming- Again dependent on the horses job the mane can be groomed to go to one side, pulled (rarely is it "cut') to length which is really just a method of trimming the mane by pulling on the hair to break or tear it at a desired length or in the case of some breeds, and employments, the mane can be roached where the mane is cut short (sort of a crew cut for horses). For what ever reason, be it looks or ease of maintenance.
Also, like human hair, if you always comb it to a certain side, it will eventually naturally go to a particular side. In regards to this too, a longer mane means more maintenance.
Cavalry mounts, will usually have a shorter mane, trained to one side or the other because of the sharper, cleaner appearance. Pack animals or draft horses will have roached manes or in some cases longer or heavier manes that are breed specific or the manes may not be as well cared for. Beasts of burden are not always treated the same as prized mounts or pets so you will see looser margins of care regarding appearance. Mostly erring to the ease of maintenance and maximize function.
Cavalry mounts will ofetn retain a mane because it is used as an aid in maintaining a seat or control. You can use it as a means to steady yourself on the horse and if you've ridden bare back its certainly a great way to haul yourself up on the horses back and stay on.
Sergey,
While definately an aesthetic observation, the horse you use in your example is an arabian. A horse breed rarely if ever, used as a pack animal or draft horse. Their manes and tails have a definate characteristic difference than the horse being used in Dan's vignette. The dished face, crested neck, "flagged" tail and longer mane are more characteristic of the smaller arabian, not the warm blood or draft of Dan's subject. The extended tail that is being held erect is also indicative of a horse that is stimulated and "proud" where as Dan's is down, exhausted or wounded.