Special Travel Pace (DMG p. 242–243):
In 1 hour, you can move a number of miles equal to your speed divided by 10 […]
For a fast pace, increase the rate of travel by one-third.
For a slow pace, multiply the rate by two-thirds.
Variant encumbrance (pn PHB pg 176) says up to str × 5 doesn’t slow speed & :
For each size category above Medium, double the creature’s carrying capacity and the amount it can push, drag, or lift. For a Tiny creature, halve these weights.
So a Riding horse has a Strength of 16, is large so that’s up to 160 pounds (16 × 5 = 80 then 80 × 2 = 160), not slowed. it has a move of 60ft or 6 miles an hour at normal pace, or increased by one-third at a fast pace (6 × 1.33 = 7.98) 7.98 or lets just say 8 for ease.
You can travel 8 hours a day without exhaustion. Plus you can gallop (inside that 8 hour limit) at double normal pace (6 × 2 = 12) for 1 hour. Makes most sense to go fast for 7 hours (7 × 8 = 56), then gallop the last hour (1 × 12= 12). For a total of (56 + 12 = 68) 68 miles a day. (A 5th the width of Florida! To do the math this horse could cross the WHOLE USA in under 31 days)
Is this right?