With Arabians, yes, line breeding is done quite frequently. It can be good and it can be bad, IMO.
The good is when the breeder, 1. Doesn't inbreed too close (full brother to full sister or son to dam) and 2. Line breeds for a reason and with horses who are correctly conformed, especially in their feet and legs.
I think that when a breeder is trying to achieve a certain "look" to her breeding program, then sometimes line breeding is necessary and fine. I DON'T agree with son breeding his dam, full brother to full sister. Too close.
The bad: In the Arab world, people are starting to breed feet problems because of all the careless breeders who just want to make a pretty foal and aren't looking at feet and legs because in the end, "It just doesn't matter". All they want is living art (I'm talking about the Show Arabian world. And of course, this doesn't apply to everyone who shows. I'm speaking generally and from experience.) Father is bred to daughter, then that foal is bred to father again. Sometimes this is a non-issue (as in, the foal will grow and be perfectly normal. But what about when that horse breeds on? )....but when the horses in question have feet problems and the breeders ignore that? Don't they realize that all they are doing is condensing the problem?
Anyway, long post from me, but I just wanted to explain some of my thoughts from the Arab Show world perceptive. Wow, thunderhooves, that second mare in the link is full brother bred to full sister. I haven't ever seen that in the Arab world. That's as close as it gets! LOL.
A good horse is worth more than riches. ~ Spanish Proverb