Is there a Scoville scale for "coldness" (e.g. mint)?

There are thermal sensation scales, and they are applied in food research too, although their primary use tends to be focused on clothing or environment. They tend to be categorical rather than ratio scales, and don't depend on the presence of a single compound the way scoville does. Despite checking several likely sources (a book on neurogastronomy, a thesis on measuring the perception of food - mostly focused on texture, but also discussing thermoreceptors) I didn't find a mention of a specific culinary scale that measures menthol concentration.

Instead of a specialized scale, industrial users of menthol products seem to simply use the relative menthol content, such as selling an essential oil that with "60% menthol". And the general public doesn't seem to have created a cult around menthol content the way it has done for capsaicine content - personally, I know more people who care for the scoville number of the chilli they are eating than people who can tell the difference between spearmint and apple mint.

I suspect that, while creating such a scale is possible, nobody has bothered to. And even if some food scientist did do it, it doesn't seem to have caught on, especially outside of professional circles.

Scoville's original method for determinig the Scoville level of a pepper was to dry the pepper, extract the heat components, and continunally dilute the extract until the majority of a panel of tasters could no longer detect it. It's not a great test, but could easily be adapted to any sort of sensation.

In the case of menthol, the majority of menthol in any detectable concentration that we encounter is added artificially so the exact menthol content is known.

The Scoville scale is a measurement of the pungency (spiciness or "heat") of chili peppers, as recorded in Scoville Heat Units (SHU), based on the concentration of capsaicinoids.

You can find a list with the concentration of menthol in plants given in ppm. Here is a list I found on https://www.naturalmedicinefacts.info/chemical/17003.html. This is a type of scale that is similar to the Scoville scale, although it doesn't use human sensation as one of the criteria.

Mentha pulegium found in Shoot max 478,000 ppm

Helianthus annuus sunflower found in Flower max 310,000 ppm

Mentha arvensis var. piperascens found in Leaf max 24,385 ppm

Mentha x piperita subsp. nothosubsp. piperita found in Leaf max 20,000 ppm

Mentha spicata spearmint found in Leaf max 15,000 ppm

Mentha aquatica bergamot mint, eau-de-cologne mint, lemon mint, orange mint, water mint found in Shoot, Leaf max 3,570 ppm

Micromeria fruticosa found in Leaf max 3,030 ppm

Pycnanthemum virginianum Virginia mountain-mint, Virginia-thyme, wild basil found in Shoot max 3,016 ppm

Pelargonium graveolens rose geranium, rose-scent geranium found in Plant max 1,852 ppm

Satureja parvifolia found in Shoot max 1,010 ppm

Hedeoma pulegioides American false pennyroyal, American pennyroyal found in Plant, Pollen Or Spore max 1,000 ppm

Pycnanthemum incanum hoary mountain-mint found in Shoot max 798 ppm

Pycnanthemum pilosum hairy mountain-mint found in Flower, Leaf max 700 ppm

Mentha longifolia Biblical mint, horse mint, silver mint, wild mint found in Shoot max 620 ppm

Pycnanthemum tenuifolium narrow-leaf mountain-mint found in Shoot max 620 ppm

Artemisia dracunculus French tarragon, Russian tarragon, silky wormwood, tarragon, wild tarragon found in Shoot max 500 ppm

Pycnanthemum muticum blunt mountain-mint, clustered mountain-mint found in Shoot max 450 ppm

Satureja grandiflora greater calamint, large-flower calamint, mint-savory, showy calamint, showy-savory found in Shoot max 420 ppm

Sideritis scardica found in Shoot max 370 ppm

Calamintha nepeta lesser calamint found in Plant max 290 ppm

Minthostachys mollis found in Shoot max 215 ppm

Pycnanthemum clinopodioides found in Shoot max 176 ppm

Pycnanthemum beadlei found in Shoot max 140 ppm

Micromeria fruticosa subsp. barbata found in Shoot max 105 ppm

Mentha x rotundifolia

found in Leaf max 80 ppm 33475 Micromeria thymifolia found in Leaf max 45 ppm

Ocimum basilicum basil, sweet basil found in Essential Oil, Plant max 32 ppm

Pycnanthemum montanum found in Shoot max 32 ppm

Juniperus communis common juniper, dwarf juniper, juniper, malchangel, mountain juniper, prostrate juniper found in Fruit max 22 ppm

Elytrigia repens couch grass, coutch, dog grass, quack grass, quick grass, scutch, twitch grass found in Plant, Rhizome max 20 ppm

Hedeoma drummondii New Mexico pennyroyal found in Plant max 10 ppm

Acinos suaveolens found in Shoot max 3 ppm

Calamintha nepeta subsp. glandulosa lesser calamint found in Leaf max 1 ppm

Rheum palmatum Chinese rhubarb, ornamental rhubarb found in Rhizome max 1 ppm