Whether or not sweat damages your hair is a matter that’s open to debate. On the one hand some saunas and steam rooms will claim that sweating can help provide your hair with oils and thereby encourage it to become healthy, but at the same time there is also the concern that the salt in your hair will soak up the moisture and thereby dry out and damage your hair.
There is some truth to both these views, and the reality is that while you might be able to provide your hair with extra oils you are probably damaging it at the same time.
A quick search in Google and you will find countless people asking how to ‘stop their hair sweating’ during exercise. Of course it’s not the hair sweating, but your head, and there is no way to stop it from perspiring (not that you would want it to anywhere). The best you can hope for is to tie your hair up and/or use a hair band to keep it away from your forehead.
Of course another option is to just avoid sweating as much as possible, and if you aren’t exercising this might mean wearing less and increasing the air conditioning in your home. When you are exercising it might mean seeking out the coolest part of the room – but you will have to resign yourself most likely to sweating at least somewhat.
Finally you can make your sweat less damaging to your hair and also your clothes, by trying to dilute it as much as possible with water. Your sweat is around 99% water and only that remaining 1% is salt, acid, bacteria etc. If you drink more water then you can dilute the sweat and it will be less damaging. However it’s important not to over hydrate either as this can lead to an electrolyte imbalance.
Really more important and the only safe and guaranteed way to protect your hair is to to get in a luke warm shower to rinse the hair straight after exercise (or whatever has caused you to sweat) and apply some moisturising conditioner at the same time which will help to give it back the moisture you may have lost.