What type of rainforest that is dominated by evergreen tree and has mild winters and cool summers?

The type of rainforest you are describing is a temperate rainforest. These forests are characterized by their evergreen trees, which thrive in the mild, moist climate, featuring cool summers and mild winters. Temperate rainforests typically receive high levels of precipitation, supporting a rich biodiversity of plant and animal life. They are commonly found along coastal regions, such as the Pacific Northwest of the United States.