It would be a common sense to have a fear of hippos so a phobia of hippos would be very unlikely. Hippos are the number one human killers among the mammals and they are very aggressive animals. They are also the most dangerous animals in Africa (after mosquitoes).
There is a word hippophobia which means "fear of horses" as you mentioned. It is because the word hippo comes from Greek which means "horse" and hippopotamus literally means "river horse". Equinophobia is used for fear of horses also.
So, there is no established term for the fear of hippopotamuses but it would be a rare case of zoophobia.
From wikipedia's zoophobia article:
Zoophobia is not the sensible fear of dangerous or threatening animals, such as wild bears or venomous snakes. It is a phobia of animals that causes distress or dysfunction in the individual's everyday life.
From the book "Anxiety Disorders in Adults A Clinical Guide" By Vladan Starcevic, MD, PhD:
Though, there is a phobia of wild animals: agrizoophobia. Most of the sources say that it is rarely diagnosed and it usually effects people in urban lifestyle. Zoos and films are common triggers.
A detailed explanation:
Agrizoophobia is a relatively common fear that is rarely diagnosed by a professional. The reason for the lack of diagnosis is simply because agrizoophobia is the fear of wild animals and is one that most modern people have.
Since this is somewhat a catch all for other phobias such as the fear of snakes there are numerous people that have some symptoms relating to agrizoophobia that could be heightened depending upon the type of animal involved. For example, someone with a fear of snakes specifically is going to react much worse to snakes than they would a wild boar.
For those with agrizoophobia often times the fear is related to the unknown or unpredictability with wild animals less than the actual appearance of a wild animal. Someone that has agrizoophobia may be afraid of rumblings in the forest but when they realize it is just a squirrel the fear may go away. This is because the unknown is often times much more impactful than the actual reality is. This doesn't mean that someone with agrizoophobia would be alright seeing a bear as opposed to hearing a the rumblings of a bear. With this particular phobia the reaction to different types of animals and the scenario around them can be very unpredictable.