I think the horse friend that you're talking about is the protector of their house or guide for her father to cross with him in afterlife.( I just kinda got the feeling because in this manga sometimes the scary looking one are the good ones or the protector like miko's friend with the octopus and the scene in the hospital idk the chapter the one who's pushing the wheelchair.) But since her father knew that there's someone lurking in the shadow (the old man ghost. I believe tht ghost is like a bad omen or bringer of bad luck so everyone that he approached will die) is after miko he can't cross to the after life since he wants to make sure that his family is safe.
Maybe the reason the dad can't going to heaven (beside something about the creepy old man ghost) is because he (and his horse friend) need to protect miko? I think the horse ghost in their home is strong ghost and since the dad befriend with it, the horsie will protect miko from bad ghost like now?