Using the language of exponential Riordan arrays, we study three distinct families of orthogonal polynomials defined by trigonometric functions. We study the moment sequences of theses families, finding continued fraction expressions for their generating functions, and calculate the Hankel transforms of these moment sequences. Results related to the Euler or zigzag numbers, as well as the generalized Euler or Springer numbers, are found. In addition, we characterize the Dowling numbers as moments of a family of orthogonal polynomials.