Some questions

So I was on the phone with my grandma and she asked me if I was either formula feeding or breatfeeding my son and I told her what one I was doing. Then she asked if I was giving him water too. My son is 3 months old by the way.

So my first question is am I supposed to bed giving him water? Because I didn’t think I supposed to yet.

Next question just my curiosity. But if we cover ourselves up at night when we go to bed and take a nap, why not the babies? Like I do get it but are t they cold too? Even with our heat on I still get cold sometimes, I do live in a winters climate.