We have conceived, built, and operated a cryogenic Penning trap with an electrically conducting yet optically transparent solid electrode. The trap, dedicated to spectroscopy and imaging of confined particles under large solid angles, is of "half-open" design with one open endcap and one closed endcap that mainly consists of a glass window coated with a highly transparent conductive layer. This arrangement allows for the trapping of externally or internally produced particles and yields flexible access for optical excitation and efficient light collection from the trapping region. At the same time, it is electrically closed and ensures long-term ion confinement under well-defined conditions. With its superior surface quality and its high as well as homogeneous optical transmission, the window electrode is an excellent replacement for partially transmissive electrodes that use holes, slits, metallic meshes, and the like.