0 Percent No Interest Credit Cards and canceling them?

My wife and I credit has always been in the low 800's(which I consider good). We have a total of 3 credit cards. Two in which we use all our purchases for and pay off each month and the other(the non interest) in which we use for things outsidte the ordinary(i.e. dental expenses, health care, trips booked online, home expenses). We usually get a 10K limit and at the most spend around 4K and each month, then I pay 200 dollars a month and at the last month of the no interest pay it off with my tax refund which exceeds the balance. Once that is done we cancel it and get another one in which is usually 12 months no interest. I heard that this can hurt your credit, but ours has remained the same. Please let me know if there is anything we should do differently. Again, need to emphasize that we keep two revolving ones open for the last 10 years which shows good payment and have no debt at all Thank you.
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Your question is, does opening and closing cards often hurt your credit. The situation you described would have a negative impact on most people, but if you make enough money and have no outstanding debt otherwise, the impact would be imperceptibly small.
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