I would say "I took a little excursion on Mount White."
Usually you don't make an excursion, and saying it was on a mountain called Mount White sounds redundant to me.
If you are referring to Mont Blanc in Switzerland, most people know it by the name Mont Blanc, not Mount White.
Sorry, it was just an example. The real context is this.
I was on holiday in Switzerland and near where I live, there is a little mountain ( the Uetliberg).
So, can I say. "I made a little excursion on a mountain called the Uetliberg)?