The existing proposals for superfluidlike spin transport have been based on easy-plane magnets where the U(1) spin-rotational symmetry is spontaneously broken in equilibrium, and this has been limiting material choices for realizing superfluidlike spin transport to restricted classes of magnets. In this work, we lift this limitation by showing that superfluidlike spin transport can also be realized based on easy-axis magnets, where the U(1) spin-rotational symmetry is intact in equilibrium but can be broken in nonequilibrium. Specifically, we find the condition to engender a nonequilibrium easy-cone state by applying a spin torque to easy-axis magnets, which dynamically induces the spontaneous breaking of the U(1) spin-rotational symmetry and thereby can support superfluidlike spin transport. By exploiting this dynamic easy-cone state, we show theoretically that superfluidlike spin transport can be achieved in easy-axis magnets under suitable conditions and confirm the prediction by micromagnetic simulations. We envision that our work broadens the material library for realizing superfluidlike spin transport, showing the potential utility of dynamic states of magnets as venues to look for spin-transport phenomena that do not occur in static magnetic backgrounds.