I tried googling up and everyone seems to suggest each one to have plus and minus of its own. Though I agree with them, I don't agree that you can choose any one as you wish. I'm telling from my experience.
Experience tells me that if one is going to spend (being physically present) the day in a temperature (avoiding the term weather because one can sit in a temperature controlled room) reasonably warmer than the room temperature, a warm bath is what I will recommend. Example, a typical Chennai or Madurai summer without air conditioner or cooler or an outdoor activity in Bangalore summer.
If one is going to spend the day in a temperature reasonably colder than the room temperature, a cold bath will help. Example, a winter in Bengaluru or native place Manipur.
Why? On a hot day, I feel more sultry after a cold shower. Similarly, I don't enjoy coming out of a hot shower in a cold weather. It makes me feel more chilling. On the contrary, body feels good coming out of a warm shower on a hot day and feels ready to face the day's heat. Same case for the other scenario of cold shower on a cold day.
A similar experience can be described travelling on a well chilled car to commute in a hot weather. The body won't like being exposed to the extreme sides from the room temperature. It can however adapt easier to one side.
It is not a surprise then that hot countries love hot beverages such as tea, coffee, etc. while cold countries love to add ice to whatever they drink. We have messed up quite a bit over time of course. Like, I hate the chilling air condition in the summer in India, because it is just plain bad for health. I usually end up using a sweater. On the contrary, I spent most of my winter back in school days where temperature was a single digit (in Imphal), I never wore a sweater to school or college. I took cold bath too, head to toe every day, even on days when I was having cold. Have I grown older? Nope. I feel the same experience when I visit Ooty hill station. I feel quite comfortable with the cold weather. But not with the chill air condition of the office.
It is worth trying for everyone :-)