The antonyms for the phrase "most hog-tied" are "free," "unrestricted," "open," "liberated," "loose," "unfettered," "unshackled," "unhindered," "unencumbered," and "unbound". Each of these words implies a sense of independence and lack of constraints. They suggest the opposite of being bound, tied up, or constrained, and instead suggest the idea of being free to explore and make choices without hindrance or limitation. Antonyms such as these are important in providing a well-rounded understanding of the meaning of a word or phrase, allowing the listener or reader to grasp the full breadth of its implications.