That is fantastic information! Thank you for letting me know.I would say no, it does not really have a cooling effect, not the one that may be anticipated by the name of the soap. In fact if you read the description on their web site, the name is only related to the lichens they use for extracting some of the ingredients, and the microclimate were they grow, in the Alps.
I classify it as a classic barbershop style soap, due to the (excellent) scent, nothing else.
Try Dinamene by Saponificio Annamaria, which to me is also better performing soap:
Benessere Naturale Shaving Soap Dinamene 125ml
Dinamene, vegetable shaving soap with extra virgin olive oil is a soap for men who like to shave in a natural and traditional way!Completely handcrafted and naturally refined three times, it is obtained from the saponification of pure vegetable oils such as extra virgin olive oil, avocado oil...pasteurpharmacy.com