Party speed is how fast a party moves on the map. It is affected by many factors, including morale, the party's highest Pathfinding skill, the amount of units in a party which are mounted, your prisoners, the terrain, day/night cycle, inventory items (e.g., iron) and weather. Note that some troops are marked as mounted in regards to this calculation even though they fight on foot, such as Hired Blades. Morale is one of the simplest factors in the equation, as it can be increased through the Leadership skill, more food variety, a smaller party size, and positive recent events such as winning battles.
If you need a quick boost to your speed to escape an enemy or catch a prime target, releasing prisoners and disbanding your own numbers will make the biggest difference in the least amount of time. Of course this method does not come without its cost.
Traveling at night, through forests, and in bad weather will slow your party down. Sometimes it is advisable to take a longer route if it means running through fewer trees.
Weight accumulated from inventory items, particularly trade goods can significantly slow your party down. It is generally recommended not to go hunting bandits while carrying a heavy load of trade goods. Beside the slower party speed, it'll limit the amount of gear you can salvage and then sell.
It's possible to counteract some of the encumbering effects of trade goods by having spare horses in your inventory, where notionally they'll carry the trade goods for you. Note that weapons and armor do not count towards your party speed, only trade goods. The speed penalty for larger party sizes is also unaffected by extra horses in the inventory.
The type of horse is irrelevant, a cheap Sumpter Horse is just as good as the more expensive varieties. However, horses themselves also slow you down, so filling your inventory with tons of horses will actually result in a negative effect.
The ideal number of horses to have changes depending on how much weight is being carried; the more weight, the more horses. The speed improvement tends to increase rapidly at low numbers and significantly slow down toward the peak, so it is not necessary to get as close as possible to the ideal number of horses. Here are a few examples however, of how many horses is the best amount depending on inventory weight:
The type of terrain parties travel over will influence their speed. Hilly or forested terrain will prevent parties from travelling at their maximum rate.