Most of my horses also aren't particularly fond of the tiger, most of the time. However, for them this directly seems to correlate with my own (lack of) enthusiasm for it. If I do it like a clicker exercise in the strict sense, rewarding for contact and approach and the raising the criteria, I lose them in no time. What works for us is when I am making mself believe that chasing the tiger is the most wonderful game ever, and that the horse is ever so cool and brave and cute and fantastic, and I am just so, so, so happy that we can play this!!!
Also, as soon as the horse has some interest in it, I am not rewarding them for "boring" things like touching the tiger but trying to find anything in their interaction with it that is cool, like stepping on it and pawing it. This, in turn, makes the game a bit more competitive, because if they stand on it or grab it with their teeth, I cannot move it. So I am getting more alert and excited, and then they do, and then I, and so we are pushing each other.
That said, we do not play with the tiger very often because for me it is hard to find that enthusiasm for any kind of "object play", and accordingly my horses find it boring most of the time as well. But in our case I know for sure that this is because of me.