If some comic book villain were to offer you the choice of freezing or burning to death, one should choose freezing, as it is probably the less painful of the two choices. However, if you are studying the poem "Fire and Ice" by Robert Frost, you are not reading a comic book or watching a simplistic movie, and thus the choices on offer have nothing to do with the relative physical discomfort involved in two ways of dying.
The poem has to do with relationships, and the extremes of "burning" with lust, represented by Frost as death by fire or living with hatred, a colder emotion. Both extremes of emotion can be painful. What Frost is suggesting in the poem, though, is not that one should choose either one extreme or the other, but rather he is suggesting that emotional extremes in general are a bad thing, by their nature disruptive and painful, tearing apart individuals and nations. Thus just as physical comfort requires a moderate temperature, somewhere between that of fire and ice, so too emotional happiness requires moderation, neither fire nor ice.