When day hiking with kids, teach them to breathe through the nose rather than the mouth when walking.Why? First, when breathing through the nose, more oxygen reaches the bottom of the lungs than if breathing through the mouth. This is more efficient for the body and so over time and so delays the onset of fatigue along the trail. Secondly, breathing through the nose rather than the mouth means less body moisture is lost, decreasing the chances of dehydrating. This is particularly the case on dry, hot days. Finally, breathing through the nose ensures that more air is filtered than when breathing through the mouth. The result is fewer irritants entering the body, reducing the chances of a sore throat once back at home.
Teaching children to breathe through the nose is fairly easy. Have them close their mouth and take in a whiff of fresh air through the nose. Then have them hold it for a moment before letting it out through the nostrils. Repeat this until the child develops a rhythm. You might make it a little fun by having them lay down and placing a bean bag on their chest. When breathing through the nose, their chest (and the bean bag) should rise and fall; if breathing through their mouth, their stomach will rise and fall more than their chest.
Read more about day hiking with children in my Hikes with Tykes guidebooks.
