It is totally possible. As you correctly noticed, at different stages of the star's evolution its spectral energy distribution changes, meaning that at some stages most energy is emitted in the infrared range, and at other stages - in visible, ultraviolet, etc. Depending on the planet's atmosphere composition, it will absorb/reflect/transmit different wavelengths with different efficiency. Atmosphere composition, in turn, depends on many factors, such as geological age of the planet, its initial composition, amount of water, presence of life, etc. In other words, the surface temperature on the planet depends on many factors that can and do change as the central star and the planet itself evolve. Consequently, the Goldilocks zone can move.