Nah, they'll be fine, well, fine-ish. The cops will see someone walking with a pack and arrest them for vagrancy before they can get into too much trouble from the elements.
But for real, I know next to nothing about this sort of thing and even I know 1. Do not fuck around with mountains 2. Do NOT fuck around with desert.
Oh, and one more thing: You're not walking to Mordor, you're walking through Mordor. There's next to no water, the water that's there is poison, the temperature swings wildly between extremes, and most of the humanoids you'll come across will get angry and violent if they see you