Grüensee is the 3rd lake along the Zermatt 5 Lake Trail, at an altitude of 2,300m. You'll reach it after about 2 hours hiking. See location on map.
The crystal-clear waters are perfect for reflecting the surrounding landscape on a calm day. It does not have any waterworks, so hypothetically you could do a brief cold dip.
We like the more quiet feeling of this lake, but the busier Stellisee is much better for Matterhorn pics.