Stamina MANAGEMENT is what is required. As long as you keep fed with the 3 best foods (use stamina-heavy foods while out exploring or doing tasks such as chopping trees)... always keep the rested buff active (if it runs out, stop and make fire to refresh it)... and refrain from sprinting every step of the way, and jumping over everything.

You don't have to walk 100% of the time, but you also should not RUN 100% of the time either.

If you are managing your stamina properly, you barely even notice any times when it is depleted... slow down a bit and make sure you keep your buffs activated, and it's not so bad.