Yes. Whilst it depends on the amount of methanol, the wattage you use on your e-cigarette, the nicotine strength, and PG/VG ratio, all menthol e-liquids provide a cooling effect on the inhale.
As you’d expect, e-liquids with a high concentration of methanol are bound to be cooler, and using a high powered e-cig device will provide a stronger menthol hit.
Menthol e-juices that contain salt-based nicotine tend to provide a cooler kick than those made with freebase nicotine. Nicotine salts allow the vapour to hit the throat and, when combined with an icy menthol flavour, they provide an incredibly chilly throat hit.
Generally, menthol e-liquid with a high PG (propylene glycol) to VG (vegetable glycerine) ratio will deliver a harsher throat hit than a vape juice with a high VG/PG ratio.