I am quite surprised that your mustang has soft feet – white or black. As Joe-Joe says, colour has nothing to do with it, rather there are other factors involved, according to several vet and nearly every shoer I have ever had.
However, of all the mustangs I have dealt with, I have yet to have one with soft feet.
My current mustang competes in combined driving, a sport requiring dressage, marathon and obstacles and twisty cones courses. The sport demands a fair amount of conditioning, for distance, aerobic and anaerobic, as well as suppleness. She goes barefoot year round.
Other mustangs I have had were Tevis Cup, endurance, 3-day eventing, and even a stadium jumper. None have even worn shoes. Quite the opposite, in fact: farriers would beg me to soak their hooves for days before their trims. One of my students has a barn filled with Kigers, some of whom do have a white hoof or two, and is also a farrier. He will tell anyone:
“and THEN you think, finally a white hoof! But nope – just as tough as any black hoof.”
Another student brings mustangs to his place for gentling, breaking and rehoming. Again, a farrier. His horses nearly all have at least 2, and generally 4 white hooves, none of them wear shoes, all the hooves tougher than the nails, he says.
With due respect to the farrier involved, I would consider some feed changes. If the front hooves are brittle, the rear soft, the whole deal sounds like a HOOF issue on both ends. Perhaps a hoof supplement might be considered?