Alcohol tends to make people feel happier and stress-free because it lowers inhibitions, lowers your heart rate, and decreases your ability to think clearly and reason. Your lowered heart rate makes you feel relaxed. When your inhibitions are lowered you are more likely to say and do things that you would not normally do. This might make people feel happier because they are not worried about what other people think.
When you are incapable of reasoning or deep thinking you might feel more relaxed because you do not worry about the day to day stresses. You may be more emotional about deeper issues however.