Idea, although not fully developed (a crappy one at it)
When skull kid said he "got rid of" Hyrule Epona, what if he did kill the Hyrule epona and replaced it with a horse that looks exactly the same, but has the same metal state as skull kid?
There was a scene in MM where they talk about skull kid (without the mask) trying to find friends, being lonely, where the faries (I tael and tatel (sp) ) find him. Well as said before, one of the Romani sisters says, "A small, lost horse seems to have been taken in by Romani Ranch, south of town..." and maybe it is not Hyrule Epona, but instead a Termina Epona? I mean, a lot of the characters from OoT to MM are different than who they were before (Sakon, for example), so how could Epona be any different?
I've noticed that a lot of MM is based on unaware vs. knowing. Clock town is chaotic freakout because they have no idea what is going on with the moon, but the other half is completley unaware of what's going on ...The Town Mayor is torn in his decision to either acknowledge or not acknowledge a potentially fatal event while The Bombers are playing their hide and seek games.
So what if Skull Kid killed Epona because she knew too much and replaced her with a horse that was lost and dependent? It would explain why she ran over to him when he came over, but didn't know Epona's song.
*shrug* It's just an idea. A crappy one at that. But I'm not going to be like "sodfsdfbfd youre wrong" to anyone, I was just putting an idea out on the table.