On woolen cloaks, walking staffs, mithril undergarments, and general fantasy faggotry, there are three things I notice immediately…
You’re not really going “old school” like you might think. In spite of how real The Hobbit and LOTR may make it seem to you, Middle-Earth never actually existed. These grand journeys where at night the little hobbits curled up in a knot of a tree's root to sleep with only their wool cloak for warmth – that never happened, m8.
People back in the day (in medieval Europe, frontier America, etc.) didn’t really do the kind of traveling into the woods for fun that we do as a pastime today. Back before cars, people who lived in cities really didn’t leave their cities too much, and leaving for pure recreation just wasn't a thing people did. People not living in cities often had access to horses. In frontier America, people who ventured out into the uncharted parts of the map had horses and wagons to transport their food, warm clothes, shelter, and other supplies. It wasn't until recently when a full overnight kit got small and light enough to fit into a backpack.
Even if people back in medieval Europe went on long excursions with minimal clothing, they would have had horses to carry their shelters and food, or at least they would have stayed at inns for the night – not camped out or carried their tents and food on their backs. You really have no idea how much a 16th century tent weighed. It simply was not possible to carry such a thing on your back. The authenticity of using a woolen cloak for modern backpacking trips today is, therefore, questionable.