Ionospheric irregularities impair Global Navigation Satellite System (GNSS) signals and, in turn, affect the performance of GNSS positioning. Such effects are especially evident at low and high latitudes, which are currently gaining the attention of research and industry sectors. This study evaluates the impact of ionospheric irregularities on GNSS positioning in Greenland. We assess the performance of positioning methods that meet the demands of a wide range of users. In particular, we address the needs of the users of mass-market single-frequency receivers and those who require a solution of high precision provided by geodetic dual-frequency receivers. We take advantage of the datasets collected during three ionospheric storms: the St. Patrick’s Day storm of March 17, 2015, the storm on June 22, 2015, and another on August 25–26, 2018. We discover a significant impact of the ionospheric disturbances on the ambiguity resolution performance and the accuracy of the float solution in Real Time Kinematics (RTK) positioning. Next, assessing the single-frequency ionosphere-free Precise Point Positioning (PPP), we demonstrate that the model is generally unaffected by ionospheric disturbances. Hence, the model is predestined for the application by the users of single-frequency receivers in the areas of frequent ionospheric disturbances. Finally, based on the observation analyses, we reveal that phase signals on the L2 frequency band are more prone to the cycle slips induced by ionospheric irregularities than those transmitted on the L1. Such signal properties explain a noticeable decline in the dual-frequency RTK performance during the ionospherically disturbed period and merely no effect for the single-frequency ionosphere-free PPP model.