Always remember that in D&D, you can mount anything. The only catch is that most of the time it will either continue on with its normal life with you on its back, or actively try and fling you off. The solution to this - as is so often the case - is to talk to your DM. read more
The description of a pegasus in the 5th edition Monster Manual says people do sometimes ride them, but as the pegasus is as intelligent as the average human and has a challange rating of 2, it would be better to think of them as an NPC who could become an ally rather than a pet/companion. read more
But he can't choose pegasus as his mount. Edit: It's also important to note that animal companions have their own statistics separate from entries as listed in the bestiary. If you look up horse there are stats for a horse as a regular combatant. If you go to the druid animal companion list it tells you all the statistics a horse companion gets. read more
{:monster {:senses"passive Perception 16", :int 10, :speed"60 ft., fly 90 ft.", :name"Pegasus", :alignment"chaotic good", :cha 13, :hit-points {:mean 59, :die-count 7, :die 10, :modifier 21}, :type"celestial", :actions [{:name"Hooves", :description"Melee Weapon Attack: +6 to hit, reach 5 ft., one target. read more