The whole point is we first need to define happiness, no?
There are a lot of people who are confused between things like sadness, disappointment, inconvenience, hopelessness and many such negative emotions.
The problem is we bundle them all en masse in to this category called 'happiness' or its opposite. To be happy is a overloaded term used to define many emotions.
Rich people suffer from the same negative emotions any human on earth goes through. Because they are humans. If their child doesn't win a soccer game, they may get disappointed, if some one in the family falls ill to a deadly disease without a cure they may feel hopeless. But these are emotions every human regardless of their financial status goes through. Whether you are rich or poor.
Having money will keep you well fed, clothed and housed. Your medical expenses are taken care of. Your children's needs are tended to and give you an overall sense of confidence and a sense of safety and freedom.
Being poor means you have a put up with a great deal of BS that life throws at you. You have to sacrifice every single thing, every single desire of yours. Its very exact opposite of what I wrote above.
I don't know of one single human who doesn't go through human emotions but yeah coming to being happy in the sense having to never really get screwed at every step along the way. Rich people never really stop being happy, and most poor people don't even what that kind of happiness actually is. Basically because they continually being fed this garbage that suffering in their current state is far better than breaking out of it.