Have you tried scrubbing while you hold them under running water?

Nikwax Footwear Cleaning Gel? Applied with a nailbrush, not the little foam thing supplied which falls off after a few applications.

Well if they were my boots...

I'd remove any excess from the surface with a blunt knife to start with. After that the only way to get it out would be to soften or even melt it and that's going to require care. Most 'how to remove wax from carpets' sites suggest using an iron with a layer of paper between the iron and wax to pull it away but I think a combination of Hair Dryer, Paper and a knife might be better.

I think this will work best with nubuck, suede or reversed leather where the outer is rough and not so well on regular smooth leather outers.

There's also industrial wax removers used by carpenters... but I have no idea what effect they may have on the leather's waterproofness and flexibility.

Ah, but most 'Nikwax' treatments don't actually involve any wax per se at all...they did originally about xx years ago. Aqueous Wax, for example is a highly fluid penetrative treatment.

Then the answer is a rotary sander! Get a nice Nubuck finish to those boots!

I was thinking a carborundum grinding wheel - great minds think alike!

I stripped all the crap off a pair of boots using alcohol,(no, not beer) and wire wool, got it down to the leather base. Tricky stuff around stitching, I used a brass wire brush on a dremmel, where you still have to be careful, as rotary brass can slash stitching.

A good long day's walk in the snow cleans up most boots a treat. Oh... but it's still August... and there's no guarantee we'll get snow this winter even if you could wait that long.

Give them a good hot shower and a lot of the crud falls off. Follow this with a hard bristled brush - repeat as necessary. Always work with my Meindls and no damage done.

Sorry did not see this. Best way to get old wax and mud off boots is warm them over the gas hob flame , when its warm wipe off with a cloth . Look like new when finished . Obviously becareful it can get very hot , and watch the rubber . Then re-apply nikwax

Isn't wax flammable. Better get an adult to help on this one.

It is but if you are careful its fine. Not set the kitchen on fire in 10 years and it makes the leather glisten like new . Cannot beat a hot wax