The Bird follows his heart by continuing to flap his wings and sing his song, trying to show that he still has hope for freedom, even though kept in a cage. The Wanderer is out riding his horse, when he comes across a clearing that is completely tranquil, and stops momentarily to watch the snow. Then he continues on his journey, and devotes himself to finish it before he sleeps.
In both instances the only one benefiting from their decision to follow their heart is themselves. They also are put in more danger from their decision, because they could be hurt more due to the fact that the Wanderer stops and refuses to sleep, and the Caged Bird keeps fighting and trying to break free of its cage.