Considering that there were Mammoths north of the wall, isn’t the Skagosi Unicorn more likely to be the Woolley Rhino?

Nope, it’s a goat:

“Far off, he could hear his packmates calling to him, like to like. They were hunting too. A wild rain lashed down upon his black brother as he tore at the flesh of an enormous goat, washing the blood from his side where the goat’s long horn had raked him.” (Jon I, ADWD)