Should I supplement 3 rail vinyl fence with electric fence?

I'm not a horse person! I am building a horse facility for my daughter. The pasture is eight acres divided into 3 paddocks. There is about 4800 feet of three rail vinyl fence.
We have an "old gentleman" quarter horse who is a lawn ornament, a sweet little "mixed" quarter horse mare, and hope to get some gaited horses with a premium on mild mannered dispositions.
Will I "need" an electric fence in addition to the vinyl fence? If so, will just placing it on the perimeter fence be enough, or should I also place it on all the interior fence as well?

Yes you will.

Vinyl fences are not very strong, a horse can walk right through one if inclined. Likely case you'll see is them reaching over/through it and accidently knocking the fence over. So your best defense is to never let them even touch that fence. Put two strings on that fence, top and bottom to keep them off. If there is a lot of spacing between rails you might have to put a third to keep them from trying to reach through the middle.

There is a vinyl "board that holds wire so it can be electrified. Vinyl fencing for 8 acres. I'd have to rob a bank to afford that but it sure looks nice. Darrin, one can buy vinyl clad lumber to eliminate painting.

I have a feeling that would encourage rot in the wet climate I live in.

Friends of mine have this & the had to add the electric wire to it, their yearling found out he can push the rails right out

I would completely replace it with electric smooth wire or at the very least, run a strand of electric all the way around on the inside side of the vinyl fence. My barn only has the vinyl fence with no electric and a I-think-I'm-a-stud-and-I-need-my-mares gelding recently ran through the fence and gashed his sides all up on the sharp edges of the broken fence. I used to like it a lot before that...

Oh, and you can get away with just adding it to the perimeter as that way at least if they run through an interior fence they are still contained. However, as I said, I'd replace it all.

One down side to vinyl fencing, it that the horses can just lean on it, requiring an electric wire.....therefore your vinyl fence is only as good as your electric wire!
Also, the other thing that bugs me about vinyl fencing, is that if it gets all warped from a horse leaning on it (because someone forgot to turn the power to the electric fence back on!) is its a bugger to get nice and straight again and because it's one whole long roll it's a pain to replace!

I like good solid post and rail, easy to source, easy to mend, strong! Plus, if someone forgets to turn the power on to the electric wire, no worries, the worst thing is a horse who decides he's going to have a chew on a post....they generally wll respect a good solid fence...and it's even better with a bit of electricity running around the top rails