Cold working or work hardening generates many dislocations which pile up and entangle this will prevent the further movement of dislocations. Try this by bending a paper clip back and forth - it becomes hard to bend at the same point and will eventually break if you continue.

How does the grain structure in a piece change due to cold work?

Cold rolling - the strip of metal passes between two rollers which exert heavy pressure. The strip is compressed and becomes much longer and thinner. The grains in the metal also become elongated. This a permanent deformation so dislocations pile up and the strenghth goes up.

What effect does cold working have on the grain size of the material?

The cold-worked structure forms high dislocation density regions that soon develop into networks. The grain size decreases with strain at low deformation but soon reaches a fixed size. Cold working will decrease ductility.