Yes Woolite laundry detergent will work in cold water.
Woolite Laundry Detergent works great in both cold and hot or warm water so you can use the Woolite laundry detergent in all water temperatures and it will clean your clothes just fine in any water temperature.
Also when you're washing new clothes for the first time, wash the new clothes separately because the colors of new clothes can run no matter what laundry detergent and water temperature you use to clean your clothes.
Woolite laundry detergent is liquid so you can use the Woolite laundry detergent in any washing machine as well as when washing any clothes or laundry.
Make sure to use the correct water temperature though to make sure you do not ruin the clothing or laundry.