Cosmopolitanism is the view that the world is a single community of humanity held together by a shared morality. This ideology stands over and against the opposing ideology that national, regional, and/or local humanity defines community. In other words, a cosmopolitan view places self first and foremost as a citizen of the world upholding universal ideals while the opposing view places self first and foremost as a citizen of a locale, be it a national, regional, or neighborhood locale, upholding ideals of self-interest. Poets, like Allen Ginsburg (1926-1997) had reputations as cosmopolitan thinkers and poets. Robert Frost (1874-1963) is harder to identify with a label of cosmopolitanism.
Frost's poetry is most famous for its inner complexities. He writes with poetic devices, simple yet emotion stirring language, and word play to create multiple levels of meaning. If read without paying attention to the various levels, built as they are around the dramatic persona, the dramatic situation, and the dramatic moment (eNotes), his poems might be understood as pleasant stories or strolls down the lane of past memories. Yet when read and analyzed from their foundational points of persona, situation, and moment, universal truths are told, universal ideals are upheld.
This thematic universality in the deeper levels of his poems raises Frost above the confines of locales. It establishes him as a thinker on global terms. In this sense, Frost is cosmopolitan. You can see from his birth and death dates above in comparison to Ginsburg's that Frost predates but overlaps with the life and career dates of poets who acknowledged cosmopolitanism. Therefore cosmopolitanism was a phenomenon of Frost's later career. His four Pulitzer Prizes and his one Nobel nomination mark him as a poet acknowledged by the world to belong to the whole world community and the world's corpus of literature. In this sense also, Frost might be considered cosmopolitan if we're using the definition supplied above.