I am scared of EVERYTHING when I am preg. I pretty much do whatever (with exceptions like alcohol and such) during the first week of the 2WW but after 6 DPO I really watch what I am doing.... so I am prob not the best person to answer.
My concern would be that animals, just like ppl, have their own moods and personalities. You'd have no way of knowing if the horse would be in a mood or get spooked and take off... or worse, kick you off. Just food for thought...