In my experience it depends on what you are washing and how dirty it is.
I was taught as a girl always to wash curtains and anything else that was dusty rather than dirty in cold water, rather than hot.
Soiled clothes, tea towels, bed linen etc. may and probably will harbour germs, both bacteria an vira as well as not becoming clean if only washed in cold water, so in the interests of hygeine either continue to wash them in hot water or scald them after washing.
Most things will come clean in cold water if you use liquid washing soap - but washing powder won't dissolve properly in cold water.
On board our motor boat I washed clothes by putting them in a square plastic box in cold water and liquid soap then puting the lid on the box. The motion of the boat while we were sailing shoogled the clothes back and forward in much the same manner as a washing-machine of the older variety did and the result was clean clothes, that had to be rinsed and wrung.
I honestly cannot see that you save water this way, but you are saving electricity for heating the water.