This nugget of advice from Rebecca Treston will change your skin and shower routine! FYI, it includes whether hot water is bad for skin
Is it bad to wash your face in the shower?
It is better to avoid long, hot showers in general because it dries out your skin by depleting the natural barrier and lipids. So, you can apply that same logic to your face.
If you take quick showers and, sometimes, it’s more convenient for you to wash your face there, then that is fine. In general, it doesn’t matter where you wash your face, as long as you wash it twice a day. Washing your face in the shower removes dirt, sebum, makeup, debris, and pollution just as it would if you washed it at the sink. There is no evidence that washing in the shower causes breakouts. If you are using an acid-based cleanser such as salicylic acid then this will help clear your acne. If you have chest or back acne, it’s a good idea to keep these acid-based products in the shower so they can be used daily on the areas of your body where you experience acne.
When using a cleanser that foams, or when removing makeup, I find it best to cleanse with lukewarm water. Hot water can dehydrate the skin, and cold water, contrary to what you’ve been told, won’t tighten your pores. If you have redness or inflammation in your skin, cool water can help soothe and reduce redness by constricting blood vessels.