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His attempts to reduce his slipping were not the most efficient; his main strategy was to make his legs stay straight, but this didn't help at all, and indeed seemed to make it even more difficult to stay upright. After a couple of moments he decided to forgo grace and let himself bend his knees, which was a wonderful modification. He was much sturdier this way, and Gotham found himself able to stand upon the ice with little incident. The youngster, standing proudly now, smiled at the stranger's remark. He was pleased that she could see his inherent fearlessness and his obvious charm. With each thing he did he attempted to be princely (when he remembered, at least), and it was quite wonderful that it was paying off. He wouldn't assume he had it down pat now, though, and would keep at it. One day, perhaps, it would become natural and completely subconcious, but for now he needed to continually practice. Eventually he would get into that sort of mindset permanently.
A wanderer was slightly different than a prince, but a prince did explore a lot, when they were looking for dragons and princesses and things. So, Gotham gave one brisk nod at her statement. "I'm explorin', ma'am!" he chimed with a grin. The youngster kept up with the politeness and formality, as this was essential when making a good impression. He needed to make a good impression, otherwise princesses wouldn't like him very much. Though this hypothesis had not been tested extensively by himself, there were many cases in the literature that it was true; storybook after storybook showed that a prince, if not nice and polite already, had to become so in order to acquire a princess. Gotham figured he'd get a head start and just be nice to begin with. In that case, he ought to say something clever and pleasant in return, so he added, "Quite lovely in here, innit!"