You see ice dams on houses without rain gutters too. To reduce ice dams add better vents to your attic so the roof stays the same temperature as the outside air temperature. Gable vents help a lot when the roof has deep snow cover. Turbine vents work too but they are noisy and don't look right on a house.
Some slope on the gutters helps the gutters drain out better, but home builders always install them level for looks rather than function.
To reduce the ice in gutters I've drilled small 1/4 inch diameter drain holes in the bottom of a rain gutters under a valley so the corner drains better in winter. I put a wood screw to plug the drain in warm weather.