In my campaign the party is going to encounter a group of Skeletons riding Warhorse Skeletons. Since I'm fairly certain that at least one of them is going to kill the rider and try to ride one of the Warhorse skeletons I thought I'd ask for advice on how I should play it out.

I was thinking to have them make a animal handling check every turn to maintain control of it and to not get bucked off. Since from my understanding skeletons in general kill the living whenever they encounter them unless given instructions not to and thus the Warhorse skeleton would actively resist being ridden by the living.

Is this a good way to run it? Or do you have a different idea?

Its fair. I doubt there is any means of healing an undead horse so once its gone, its gone. On top of that, such a horse would cause a fuss in most cities unless this is a homebrew world. 

It depends on what you want to have happen.

You are right, the undead typically despise the living and try to kill them whenever they can.

If you want them to ride skeleton warhorses because you think it's cool, you can rule that the animal instinct they once possessed can be harnessed and the creature can be tamed.

Should you prefer your group to not have an undead steed, you can simply have the skeleton warhorses keep bucking and fighting and biting.

In either case, should they encounter 'normal' folks on the road or in towns/cities, the undead should probably still try to kill all those.

If it was my group and if I wanted to permit them to have the new mounts, I would ask them to capture control of the undead, first. If I really wanted to make it easy for them, I'd ask them to cast Animate Dead, and follow the rules given there to maintain control.

Knowing me, however, I'd require them to find a rare ritual or magic item with which they first have to make the horses submit. Or if there is a legit spell that can wrest control of an undead from someone else, I'd go for that.

There's a level 14 feature for Necromancer wizards Command Undead.

Either that, or a ritual or magic item that duplicates it, is what I'd need from my players...

Thanks for the advice.

For the encounter I have planned the skeletons are going to use their mounts to keep away from the party and pepper them with arrows since and since the party is mostly melee focused I expect one of them to try to hijack a mount from one of the skeletons.

I mostly just want the mount to be usable for the encounter but be a pain to keep using after it finishes.

I think skeletal mounts are cool and fun. If you want to make them a temporary fun thing, tie the mounts' existence to the skeletal riders. Once the riders are destroyed, the mounts begin to slowly deteriorate. That way, the party can use them for however long you want, but next minute/hour/short rest/long rest/day/whatever the mounts revert back into a pile of bones. Let the players know this too. As soon as the encounter is over, make the deterioration effect obvious pretty quickly so the players don't feel blindsided when the mounts stop being viable later on.