In Dungeons and Dragons Firth Edition (D&D5e), horses are considered to be of large size. Well Centaurs are considered Medium size. Does this mean a lot of difference in perspective to game play? No. What it does mean is representing a character (or creatures) facing.
Medium creatures are thought to fill a 5 foot by 5 by 5 foot space
Large creatures are thought to (mostly) fill a 10 foot by 10 by 10 foot space
Huge creatures (mostly) filling a 15 foot by 15 by 15 foot space
A monster can be Tiny, Small, Medium, Large, Huge, or Gargantuan. Table: Size Categories shows how much space a creature of a particular size controls in Combat.
|Tiny||2½ by 2½ ft.||Imp, Sprite|
|Small||5 by 5 ft.||Giant Rat, Goblin|
|Medium||5 by 5 ft.||Orc, Werewolf|
|Large||10 by 10 ft.||Hippogriff, Ogre|
|Huge||15 by 15 ft.||Fire Giant, Treant|
|Gargantuan||20 by 20 ft. or larger||Kraken, Purple Worm|
Most creatures are Medium sized (5 foot by 5 by 5 foot). Lets say the PC is a 10 ft tall Goliath, they still would be considered medium as they take up 5 foot by 5 by 10 foot.
Horses would be 5 by 10 by 10, and could be argued as being either Medium or Large – but because we commonly ride them its better to have them as large – 10 by 10 by 10.
Centaurs being a playable race, they are made to be Medium in size for convince – you don’t want you’re PC to have a 10 by 10 facing, it makes it to easy to be surrounded and makes moving through spaces to difficult.
D&D5e doesn’t have a system of differentiating the half sizes (you’re either a size or not) and the only mechanic for size is facing (and dismounting if you’re Mounted)