It's not, compared to the pacific northwest. I recall taking photos on my first visit to an Oregon university because they _obviously_ were watering their lawn in the winter to keep it that green instead of letting it go dormant.
A large sliver of the PNW is temperate rainforest, so yes. When you have areas that get 100-170 inches of rain a year (e.g. Olympic peninsula area), it's probably going to be very green at that point.
Other than during the spring, most of TX is not particularly green (to put it charitably), even by the coast where it rains more.
Source: have lived there for a long time
The Eastern part of it is classified as humid subtropical. It is indeed very green. See https://en.wikipedia.org/wiki/Climate_of_Texas#Piney_Woods for verification and https://www.pinterest.com/CollyBlackSheep/east-texas-piney-w... for plenty of acceptably green pictures.