Horses move 11 parts per day ( Travel and Exploration Rules)
Rolling a Horse
To generate a newly freed horse, roll the following (13) steps to modify the default stats in the PHB for riding horse:
(1) Roll hit points as 2d10+2, modify if the Con modifier changes, see below.
(2) Roll 1d20 for speed modifiers. 1 is -5ft, 19-20 is +5ft
(3) Roll 1d20 for Strength modifiers compared to normal. 1-4 is -1 to the modifier. 17-20 is +1 to the modifier. Thus, 17 would be 18 or 19 Strength, but it’s recommended for 17-18 to be 18 strength and 19-20 to be 19 Strength, unless flavor strongly suggests otherwise.
(4) Roll 1d20 for Dex modifiers. 1-4 is -1, 17-20 is +1 (both vs normal)
(5) Roll 1d20 for Con modifiers. 1-4 is -1, 17-20 is +1 (both vs normal)
(6) Roll 1d20 for Horse intelligence. 1 on 1, 3 on 17-20, 2 otherwise.
(7) Roll 1d20 for Horse wisdom modifiers compared to normal: 1-4: -1, 17-20: +1
(8) Roll 1d20 for horse charisma modifiers compared to normal: 1-3: -2, 4-6: -1, 7-13: +0, 14-17: +1, 18-20: +2. Yes, this means a roll of 1 means the horse has a Charisma of 2.
(9) Roll 1d20 for objective horse attractiveness. Interpret the results, but record the number as well.
(10) Roll 1d10+12+Wis mod + Cha mod for horse orneriness…gives a PHB standard horse an orneriness of 15
(11) Roll 1d10 for morale. 1 is Morale 16, 2 is Morale 15, 3 is Morale 14, 4 is Morale 13, 5-6 is Morale 12, 7-8 is Morale 11, 9 is Morale 10, 10 is Morale 9. Subtract 2 from Morale once the horse is tamed. +2 morale for wild, -2 morale for tamed.
(12) Roll 1d20 for horse athletics. 17-20 has proficiency to athletics. 1-2 disadvantage.
(13) Roll 1d20. Report 1s and 20s to James E to give the horse an extra random flaw / perk.
Training a Horse
Note: training a horse improves morale, as above, and makes the failure case for failing morale less bad. Additionally, only trained horses and warhorses can wear barding.
Horses and Terrain:
You can ride a horse at full speed through easy terrain (plains or light snow), or 3/4 speed through normal terrain (light forest, thick snow, or non-steep rocky regions). You can guide a horse at your walking speed through tricky terrain (swamp or slightly steep mountainous areas). You can guide a horse at a slower speed through very tricky terrain (dense forest). You can guide a horse over moderately steep areas with an animal handling check.
In combat, horses have a move speed of 60’ on easy terrain, 45’ on normal terrain, 30’ on tricky terrain, or 20’ on very tricky terrain. Horses cannot be taken over steep areas in combat.
Horses on Expedition
Horses don’t get perception checks if in a party.
Horses on expedition require either feed or extensive grazing time. Horse feed costs 1/4 gp and weighs 5 lb / day.
Note: lower morale is better. The horse has to roll 1d20 and beat its morale to avoid spooking. An animal handling check can also be made. A wild horse has morale 14. A tamed horse morale is 12. Trained is 10. Warhorse morale is 8. (all normally).
Note: orneriness sets the animal handling DC of most activities (benchmark, can be higher/lower). If you fail by 5+ the horse gets to do its own thing.
Note: horses don’t get perception checks if in a party.
Note: a horse raised from being a foal is highly trained, morale 8, like a warhorse (warhorses have to be raised from birth).