QCS Vostok
Just an idea which I haven't tried, but wonder how it would turn out if you got an unscented shaving cream tub (probably harder to do with a soap), and added a bit of mint essential oil? I've now interested myself in this, so I may have to give it a shot!
The wrapper on vintage Williams soap used to recommend adding Aqua Velva to the soap before lathering.
That is definitely an option, and if you're feeling really hardcore, you can order your own menthol crystals and make a face-freezing version.