If uninsulated wire is used the electricity will run across the windings(ie; current will not go in circular way, instead it will leak into net loop since no insulation is there) and not make loop after loop and create a magnetic field.
If there is no insulation the resistance to the flow of electricity will be reduced to almost zero. Too much current will be drawn and the fuse will be blown or the circuit breaker may be tripped.
This shows that an insulated copper wire is used in an electromagnet.