Ice builds up on exterior of house during winter?

There is a flat portion of my roof that has electric wires to melt the ice and snow during the winter. when the water melts…it runs down the side of the house and re-freezes on my ceder shingles. i am worried that it may try to run under the shingles and force its way back into the house. any thoughts? should i be concerned? there are no gutters on this side of the home, should i install them and use electric wires inside the gutters to stop the melted water from running down the side of the house? any other suggestions?