The only ingredient of pure neatsfoot oil is the oil rendered from the legs/feet of cows - a neat is an old english term for a cow. Mineral oil is a by-product of distillation - the two are not alike at all.
The old leather scales were made by a cuir bouilli technique - heat and pressure. The leather was boiled, then pressed into shape in moulds. Depending on the time of immersion in boiling water and whether the mould was heated and to what temperature the mould was heated, the leather is stiffer or more supple. At high heats fibres within it actually polymerise and flow like resin, giving an almost plastic/rubber look and feel to the leather.
Some techniques employed wax - instead of boiling the leather was baked, then dunked into molten beeswax, resulting in a very tough leather. This type partially softens in heat, and can be reheated and reshaped.
Other techniques used a glue, made from pigs feet.
It is usually hard enough to resist most forms of wear (it was originally used to make armour - some types were said to resist iron penetration), and using conventional leather treatments on it can cause it to degrade over time - depending on what type of process was used to harden the leather in the first place. If it is very hard and polymerisation of the fibres has taken place, treating it with dressings, etc, will not work - they simply cannot penetrate far and build up on the surface. Some moisture content is essential in leather - it goes brittle and cracks when all the moisture goes - and flooding the surface with oil can form a barrier to the atmosphere that stops the leather self-regulating, leading to it becoming brittle.
Conservationists usually remove recently applied dressings with alcohol or benzene.
None of which helps the original OP. Using some form of wax would be better than the solvent action of oil, which might soften wax-treated cuir bouilli, but its not recommended in the long run - how 'long' that period would be is hard to guess, though - maybe not a problem if its another hundred years or so!
Regards,
Neil