Cold sensations of varying intensities are perceived when human skin is subject to diverse environments. The accurate presentation of temperature changes is important to elicit immersive sensations in applications such as virtual reality. We developed a method to elicit intensity-adjustable non-contact cold sensations based on the vortex effect. We applied this effect to generate cold air at approximately 0 {\deg}C and varied the skin temperature over a wide range. The perception of different temperatures can be elicited by adjusting the volume flow rate of the cold air. Additionally, we introduced a cooling model to relate the changes in skin temperature to various parameters such as the cold air volume flow rate and distance from the cold air outlet to the skin. For validation, we conducted measurement experiments and found that our model can estimate the change in skin temperature with a root mean-square error of 0.16 {\deg}C. Furthermore, we evaluated the performance of a prototype in psychophysical cold discrimination experiments based on the discrimination threshold. Thus, cold sensations of varying intensities can be generated by varying the parameters. These cold sensations can be combined with images, sounds, and other stimuli to create an immersive and realistic artificial environment.