Final answer:
The boys' excitement could be due to the adventure of the task, seeking paternal approval, or imitating their father's hardworking legacy, which instills a sense of gaining independence and responsibility.
Step-by-step explanation:
The boys' excitement about their father's order to make a path through the snow could be linked to several emotions or motivations derived from the context provided. For example, the prospect of undertaking a challenging task, the sense of adventure that comes with a journey, or the emotional response to their father's command in an atmosphere of strict parenting can all contribute to their excitement. However, without a specific text reference that directly explains the boys' feelings, only assumptions can be made. The importance of paternal approval, particularly where the father has a significant status or legacy as indicated in the reference to 'paternal affection', may also play a role in their willingness to undertake difficult tasks. The boys might also associate the clearing of paths as a step towards gaining independence, responsibility, and strength, much like their father who 'laid the foundations of his fortune by hard work.'