Do I need to have waterproof jacket with hood, over-trousers, spare warm clothing and hat and gloves?
Yes, mountain weather can be highly changeable even in the height of summer. Just because it is warm and sunny at the bottom of a mountain does not mean it will stay the same all the way to the top. Generally it gets approximately 1 degree C colder every 100m you climb. Waterproofs keep you much warmer by protecting you from the wind, which also increases with height. Spare, warm clothing including hat and gloves must be carried in addition to waterproofs for these reasons.