Well, I thought that the homozygous recessive would definitely be the answer. I assumed they wanted you to say
let O = normal, let o = disease.
By definition, if they are homozygous dominant, then they are normal - meaning they carry no traces of the disease, therefore even if they were homozygous, it doesn't matter because they are homozygous normal. Therefore, by definition, a homozygous normal hourse isn't going to drop dead at birth just because it had a homozygous genotype. That's what I think at least, -shrugs-
Also great news about the structure question! 
That's what I got too, and what a lot of other people wrote as well.
Btw, it's not a specific horse
species it's a particular
breed (same species). Therefore, all horse breeds would have to be heterozygous if this was to occur. The inference that was meant to be made is that because she's heterozygous and unaffected, the trait must be recessive. This was probably an unfair extrapolation to ask of students who have only completed Unit 4 biology, but nonetheless, it was the one to be made.
All this information about OWLS being both dominant and recessive is irrelevant. When considering the trait,
lethality it is most definitely recessive. The fact that it shows aspects of incomplete dominance in
other traits (ie. overo colouring, frailty) is irrelevant when only considering this one trait.
I agree, the question was ambiguous as fuck and asked a lot of students; but I don't think the other answer is plausible... sorry x_x (Just my opinion)