B. is extremely excited to go to the castle with Miss Miller.
Explanation:
Based on the interaction between Miss Miller and Winterbourne, it can reasonably be inferred that Winterbourne "is extremely excited to go to the castle with Miss Miller"
From the excerpt, we can infer that Winterbourne has the idea of going to the castle with Miss Miller. This is seen in his response when Miss Miller's brother, Randolph showed no interest in going to the castle. But for Winterbourne, he is extremely excited to go to the castle with Miss Miller. He wasn't seeing himself staying back with Randolph.
