The 52-year-old man was also arrested on suspicion of attempting to cause criminal damage. He has been released from custody.
It comes as the video was widely shared on social media following the match at Fratton Park which ended in a 4-0 defeat for the Blues.
Footage shows the man swing at the horse named Luna, who was uninjured, before scrambling to outrun the animal– but failing to do so.
She is a Hampshire and Thames Valley police horse from the joint operations unit.
Hampshire police confirmed five arrests were made, including over the horse incident.
Saints fan Dean Baigrie, 40, of Taplings Close, Winchester, has been charged with possession of a firework/flare at a sporting event and throwing a missile onto a football playing area.
He is due to appear at Portsmouth Magistrates’ Court on October 31.
Two Portsmouth fans, an 18-year-old man and 19-year-old man, both got a conditional caution for public order offences.
A third Blues fan, 20, was arrested on suspicion of a public order offence. He was later released with no further action to be taken.
Assistant chief constable Scott Chilton said: ‘Our priority was to keep people safe and I’m pleased to be able to say this morning that our policing operation has achieved that.
‘We knew that the majority of fans wanted to enjoy this match without having to worry about their safety and we did want we felt was needed to reassure them.
‘Sadly we had to prepare for the potential that a minority would try and ruin it for everyone else and this required us, in conjunction with both clubs and our partners, to put plans in place to ensure we were ready to stop that.
‘As expected, due to the nature of the routes to and from Fratton Park, there were times were groups of opposing fans came into close proximity to one another.
‘However, as a result of our careful planning we were able to keep these groups apart and get them to and from the stadium safely.
‘I think the fact that we have had no reports of anyone being injured and only a few people arrested is testament to the hard work that everyone has put into this operation.
‘I would like to thank the fans for supporting our officers throughout the day and for those who helped us during the planning process.’
Police initially said the man arrested over animal cruelty was 42.