Yes, they are COLD! Whew!

I think it is the adhesive, not the lidocaine. It is an aqueous based gel, and much different from other adhesives we are used to. The moisture in them would be room temperature and feel cold. When they get "old" they are not so cold and also don't stick as well
(not that they stick "well" in the first place ). They can be reactivated, with some misty moisture, like in a steamed up shower sitting on a counter, or a blast of steam from a tea kettle.

If you leave them out in a humid place they will swell up and become very strange looking. I left a used up one on our dock upNorth one morning, it was sort of folded in half with the sticky parts together, and by noon it had swelled up into a gooey mess!
It was overcast and foggy that day.

I find they feel the coldest when applied to my back. And I don't have any numbness there at all.