The benefits of cold showers are massive. First of all they give the body some positive stress. Right now, as a collective, we are way too comfortable (food, temperature, essentials) and this is not exercising our positive stress mechanisms. We have tons of negative stress, but not enough positive stress.
When you flood the body with cold water, the lymphatic system and capillaries constrict, and they get a workout. This makes them stronger and allows them to dump toxins and more effectively circulate blood. Also, cold water balances the endocrine system (adrenals, thyroid etc), and reduces inflammation.
The craziest thing is that when I take a hot shower, I feel cold afterwards, but when I take a cold shower, I feel warm for the rest of the day. Cold showers/cold water therapy forces you to learn how to create inner heat.
One of the biggest benefits I have found from cold water therapy is that it stimulates the production of testosterone. I have definitely felt an increase in T since starting cold showers a year ago. Cold showers also really help you penetrate fear and train yourself to have delayed gratification.
Overall, cold showers are a bad-ass way of stimulating and improving the bodies natural healing mechanisms!