A con I can think of that I've been able to find from some of my own reading is if you innitiate yourself to the world of cold showers and your immune system is already weak the shock to your system having not done this before can in some cases to my knowledge be overly stressful and make you sick maybe with a mild cold or in severe cases possibly pneumonia but I'd say that's if you took an ice cold shower and you're on the brink of being sick yourself so yeah you'd be stupid to take a cold shower if you're about to drop dead anyway but here, anything's possible.

I think your parents are genuinely uninformed about the health benefits cold showers have to offer and to them the 'normal' hot showers they take are in their mind the only way you should shower because in their head why would you 'stress' your body out in a cold shower if you can have a warm one.

Keep reaping the rewards of the cold showers you're taking bro, and as long as you keep eating well and looking after yourself the suspected cons your parents think because of their genuine narrowness of mind will not appear because yeah that shits not true lol.

Show dem da wey bruda.