Because the light in most covered arenas is so bad, many equestrian photographers do use strobes hung from the ceiling. Especially in western events. I don't want to do them bad enough to go to the trouble.

Most agility will not want you using on camera flash on their dogs. Strobes are different and I think most are ok with them. Though, like Jim said, I don't know of any agility photographers who use them.

My honest opinion is if the light is that bad, don't even do it. It won't be worth the time and effort for what the end product will be like

I am envisioning the poorly lit covered horse arenas that are open on the sides. So, all this light streams in and blows out the background and you have a poorly lit shot

Now, if it is indoor and has decent light, go for it with a 2.8 lens