Stair Ambulator (5e Feat)
From D&D Wiki
Prerequisites: hooves, or a steed with hooves
Allows a character to bring a creature with hooves into a dungeon, or ambulate stairs in a dungeon for a creature that has hooves.
If you have hooves, you can ambulate stairs at half your normal speed rounded up to the nearest 5 ft. If you do not have hooves, you can bring a trained creature with hooves at half your normal speed rounded down to the nearest 5 ft.
This feat works in any area where there are stairs, in dungeons, inside buildings, in cities etc.