When speaking of "cold" water for laundry, the accepted temperature from most sources is around 85F, which feels slightly "cool" rather than totally ice cold.
Most washing machines with automatic temperature control aim for an 85F wash temperature when set to "ATC/Cold". Tap cold is just that, whatever one gets from the tap.
One reason for the growth in liquid laundry detergents is that unlike powders, they disslove in cold water, and will not leave a powdery "residue".
Again, rather than depending upon washing soda, and other alkaline substances for cleaning, liquid laundry detergents rely upon surfactants, and increasingly enzymes to do the job.
This is why some feel liquid detergents are better on oil/grease soils,while powders on clay based dirt. However testing on both sides of the pond by various independent agencies shows little difference in cleaning performance between TOL liquid detergents and powders.
One says "TOL" because until recently, many liquid detergents were mostly water, indeed some BOL and even MOL products on the shelves today are still mainly water. On the other end of the spectrum we have the opposite extreme, liquid detergents with so little water they are now gels.
Yes, laundering in cold water does require stronger detergents, or more of the product as two of the five variables in good laundry technique (water temperature and energy),have been reduced. This can be the cause of the gunk, mould and filth some complain their washing machines become full of when doing cold water washing with liquid detergents. There either isn't simply enough power in product, or the concentration in the wash bath is not great enough to remove soils and keep them suspended, so the muck ends up clinging to everything.
Think of it as washing greasy dishes in cold water. If you use enough of a strong degreaser, oils will disslove and wash away, not clinging to anything. Use too little and the stuff clings to the sides of the sink and even recoats the same pan you just washed.