Using dynamical computer simulation we have investigated vortex matters in glass states. A genuine continuous depinning transition is observed at zero temperature, which also governs the low-temperature creep motion. With the notion of scaling, we evaluate in high accuracy critical exponents and scaling functions; we observe a non-Arrhenius creep motion for weak collective pinning where Bragg glass (BrG) is stabilized at equilibrium, while for strong pinning the well-known Arrhenius law is recovered. In both cases, a sharp crossover takes place between depinning and creep at low temperatures. The possible relation between the present results and a recent experimental observation of a second-order like phase boundary inside the BrG phase is discussed.