Reaching a ground state of a spin system is analogous to a protein evolving into its native state. We study the `folding' times for various random Ising spin systems and determine characteristic temperatures that relate to the `folding'. Under optimal kinetic conditions, the `folding' timescale with the system size as a power law with a non-universal exponent. This is similar to what happens in model proteins. On the other hand, the scaling behaviour of the characteristic temperatures is different than in model proteins. Both in the spin systems and in proteins, the folding properties deteriorate with the system size.