No, melting is not a chemical reaction. Melting is a change between phases of matter, and it does not involve the breaking or formation of any new chemical bonds. As the temperature increases to cause a substance to melt, the arrangement of the molecules in the solid/liquid changes, but no chemical reaction takes place. The same is true for liquid to gas phase changes as well as for the reverse processes (freezing and condensing).
Everyone is familiar with rust, which is what happens when iron oxidizes—the result of iron being exposed to water and oxygen.