We report the first observation of inverse magnetocaloric effect (IMCE) in hydrothermally synthesized single crystalline La0.5Sr0.5MnO3 nanowires. The core of the nanowires is phase separated with the development of double exchange driven ferromagnetism (FM) in the antiferromagnetic (AFM) matrix, whereas the surface is found to be composed of disordered magnetic spins. The FM phase scales with the effective magnetic anisotropy, which is directly probed by transverse susceptibility experiments. The surface exhibits a glassy behavior and undergoes spin freezing, which manifests as a positive peak (T(L) ~ 42 K) in the magnetic entropy change (-ΔS(M)) curves, thereby stabilizing the re-entrance of the conventional magnetocaloric effect. Precisely at T(L), the nanowires develop the exchange bias (EB) effect. Our results conclusively demonstrate that the mere coexistence of FM and AFM phases along with a disordered surface below their Néel temperature (T(N) ~ 210 K) does not trigger EB, but this develops only below the surface spin freezing temperature.