Mount&Blade/Mounted

Riding a horse gives you an instant advantage against foes on foot, and adds another level of depth to gameplay.

Weight isn't an issue
The most important factor is that when riding the weight of your equipment has no real effect on the horse's speed, and so it is only the speed of the weapons and shields themselves that slows you down. This means you can fight efficiently while wearing full black armor, whereas if you fought on foot you'd barely be able to move at all without putting points into Athletics.

Controls
The horse controls similarly to being on foot. WASD control the horse's speed and direction while controls your character's aim. There is a blind spot behind your left shoulder where you cannot aim (when aiming into this blind spot with a ranged weapon the targeting crosshair will quickly disappear).

Directional swings
Just like on foot, with a one- or two-handed weapon you can choose what side to swing to simply by looking at that side. If you keep missing or swinging from the wrong side you can swing your weapon back early, but bear in mind that this leaves you open to attack. Also, more of your weapon is exposed when on your right side than your left, so if you have a choice it's best to pass to the left of an enemy while swinging from the right for the best chance of dealing damage.

If your horse has stopped you can also stab and chop.

Weapon choices
Unlike on foot, the length of your weapon is absolutely crucial. While fighting with a short sword you will have to get dangerously close to your enemies which will likely result in damage to both you and your horse. If you have a choice between a short weapon with good damage and a long weapon with mediocre damage, the long weapon is always the best choice.

The overall best one-handed weapon is the Bastard Sword. It has immense length, great damage, and decent speed. The Bastard Sword can also be wielded as a two-hander (simply put your shield away) but the Sword of War is an even more powerful two-handed sword.

On horseback, the main difference between one- and two-handed weapons is whether you want a shield. While a two-hander is slightly longer and deals a good deal more damage the shield provides extra protection, and since you're only swinging the two-hander with one sword there are speed and damage penalties which further narrow the gap.

If you want to do both, try building up your proficiency wielding two-handed weapons with some points in one-handed as well, and then using a Bastard Sword and a shield. For most killing put your shield away, but whenever you need it just pull it out again. This way you will fight with a slight disadvantage when using the shield and also cannot access the greater damage of the Sword of War, but you still get the advantages of having a shield quickly accessible. You will have to put some points into Weapon Master if you want to keep your one-handed skill at a comparable level to your two-handed skill, although once you reach around 150 most enemies will go down quickly anyway.

Horse choices
If you like the idea of running your enemies down with a lance or outstretched sword then what you're looking for in a horse is speed above all else. Speed has a direct effect on damage; the absolute best horse for this is a Courser (preferably Spirited), however it doesn't have much armour and may stop if it runs into enemies at lower speeds.

If you would prefer durability over speed-based damage go for a Warhorse or Charger. These horses are extremely expensive, but they have an immense amount of armour and may be even harder to kill than you! They will run straight over anything other than obstacles, horses, or friendly forces, making them perfect for dashing into dangerous throngs. If they do stop, however, their slow speed means it can take a while to escape from the situation.

The other horses fall somewhere between these two extremes. These particular three horse types are very expensive (especially the Charger) so if you start losing them in combat you may want to try different ones until you find one that matches your fighting style. The maneuverability of the horse is of less importance than its speed, as with a fast horse like the Courser you can slow down, do a 180°, and then head off again, only being in danger for a very short period.