Static reactive metasurfaces allow excitation and propagation of surface waves. In this paper, we theoretically elucidate how surface-wave propagation along a reactive boundary is affected by temporal discontinuities of effective parameters characterizing the boundary. First, we show that by switching the value of the surface reactance, the velocity of surface waves is fully controlled, and the power of reflected and transmitted surface waves can be amplified. Second, we indicate that when a boundary supporting waves with transverse-electric polarization is switched to the one allowing only transverse-magnetic polarization, the propagating surface wave is "frozen"and converted to a static magnetic-field distribution. Moreover, efficiently, these fields can be "melted", restoring propagating surface waves when the boundary is switched back to the initial state. Finally, we demonstrate that temporal jumps of the boundary reactance couple free-space propagating waves to the surface wave, in an analogy to a spatial prism. All these intriguing phenomena enabled by temporal discontinuities of effective properties of reactive metasurfaces open up interesting possibilities for the generation and control of surface waves.