We always used small wood screws to secure shoe plates (not cleats), although previously I have ridden wet races with the nails conveniently into the soles of my feet, but never felt them in the cold conditions.
No surprise I have had to get an automatic car because feet do not have the correct nerve response.
You could make sensible shoe plates from a bit of old shoe leather.
I eventually went on to screws as well but when the sole became very wet after a rainy ride the leather could swell and seemed to loosen the screws somehow. There were some commercial leather shoeplates at one time I seem to recall. I need to look in my 'Holdsworthy Aids' files!
EDIT - yep, Cliff Peters made some but they still had an alloy 'slot' embedded in the leather. There were some solid rubber ones as well.
I've got a pair of NOS 'Anquetil' long ones in my 'stuff' still in the packet.
Today is the yesterday of tomorrow.