For optimal cleaning results, water temperature must be above 15C (60F). Otherwise the ingredients in most laundry detergent will not activate.
In other words, if your water is too cold, your detergent won’t work.
Wash your hands under the water; if the water is too cold for your hands, it is likely too cold for your washer.
A problem I have been seeing in increasing numbers is flooding caused by cold water washing (even those using cold water detergent). The fill mechanism has a small hole, which gets clogged up with soap scum/residue that’s not washed away in the cold water.
Make sure your detergent is for cold-water use and make sure you use hot once a week (minimum) to clean out the detergent residue. Also see comments on detergent residue in clothes and it’s effect on your skin and your health.