In the UK, we would say "Have a great summer holiday" or "Enjoy your summer holidays". Whether we say holiday or holidays depends on what we mean. "A holiday" is a period of time spent away from your home, perhaps in a different country, lying on a beach or skiing (for example). "The summer holidays" usually refer to the six-week period in the summer when children don't have to go to school.
We don't usually say "Happy Holidays" at any time of year. Various politically-correct councils etc have tried to introduce this phrase in the last few years, because they seem to believe that saying "Happy Easter" or "Happy Christmas" offends non-Christians! The phrase has not caught on, thankfully!