In D&D 5e, the daily rate of mounted overland travel is generally the same as on foot, because horses get tired and adventurers carry a lot of heavy equipment.
See the section Special Travel Pace in the DMG (p. 242–243). This section starts:
The rules on travel pace in the Player’s Handbook assume that a group of travelers adopts a pace that, over time, is unaffected by the individual members’ walking speeds. The difference between walking speeds can be significant during combat, but during an overland journey, the difference vanishes as travelers pause to catch their breath, the faster ones wait for the slower ones, and one traveler’s quickness is matched by another traveler’s endurance.
In the same section, the rule is:
- In 1 hour, you can move a number of miles equal to your speed divided by 10.
and then:
- For a fast pace, increase the rate of travel by one-third.
- For a slow pace, multiply the rate by two-thirds.
So an unencumbered horse with a speed of 60 could theoretically travel 6 miles in an hour at a normal pace. At a fast pace (a gallop), 8 miles per hour. That's "twice the usual distance for a fast pace", where "usual" means a creature with a speed of 30. This suggests that a riding horse with no rider, traveling alone, can cover 48 miles per day at a normal pace.
So the rule that "a mounted character can ride at a gallop for about an hour, covering twice the usual distance for a fast pace" seems to exist to allow for mounted travelers covering short distances quickly by using the mount's speed instead of "the usual pace", for up to an hour each day.
So, according to the rules, a traveler on a horse at a normal pace (3 miles per hour) will cover about 24 miles in an 8-hour day. If you make the horse gallop for an hour each day (fast pace for a horse being 8 miles per hour), that range increases to 29 miles. That's within the realm of what you would expect in real life, with a fast horse on good roads in fair weather.
Variant: Encumbrance
If you're using the encumbrance rule, a Riding Horse needs to be carrying less than 80 lbs of rider and equipment to get its full speed of 60. Loaded with between 80 and 160 lbs it has a speed of 50, and carrying between 160 and 480 lbs (its maximum carrying capacity) it has a speed of 30. A 200 lb adventurer in chainmail with a dungeoneering pack, longsword, and shield weighs in at about 325 lbs, so under this rule a horse's travel pace is usually the same as an unencumbered adventurer on foot.
Normally if involved in an activity during travel a character cannot participate in perception checks to, for example, notice when they are being followed.
As adventurers travel through a dungeon or the
wilderness, they need to remain alert for danger, and
some characters might perform other tasks to help
the group's journey.
Characters who turn their attention to other tasks as the
group travels are not focused on watching for danger.
These characters don't contribute their passive Wisdom
(Perception) scores to the group's chance of noticing
hidden threats. (PHB p.182-183)
A ranger with this ability may be engaged a travel activity (e.g. foraging, navigating, tracking, creating a map, ...) while still being allowed to participate in the party's perception checks.
You gain the following benefits when traveling for an hour or more:
...
- Even when you are engaged in another activity while traveling (such as foraging, navigating, or tracking), you remain alert to danger.
Best Answer
Travel is ended by entering combat or any other sort of tactical movement (Where a character's speed is used)
"Travel" Refers to the movement mechanics described on page 181 of the PHB.
At the start of Chapter 8: Adventuring, the PHB defines the rules for traveling and movement in scales of days, hours and minutes. Here, you can also find the Travel Pace Table and the Activity while Traveling sub-section.
Traveling applies while the above rules are being utilized. In other words, the players are considering to be "Traveling" whenever they are moving and are outside of combat (Where the combat movement and round rules are used), and this includes navigating a dungeon. This is the same condition for being able to perform any of the Activites while Traveling.
The smallest unit of time in the Travel Pace table is 1 minute, so this is the shortest allowed one for traveling. In order to travel, a Travel Pace must be established, so this rules out any sort of tactical movement.