Do you know what is wrong with the construct "My dog won't let me touch its feet (or tail, or face)"?
Everything is wrong, on three different levels.
1. Foundation: your relationship with the dog is not built on trust
The first thing I do with every dog I get is brush it. It does not matter whether it is short-haired, wire-haired, or long-haired. What matters is that the dog immediately starts learning that this is routine and normal, and, ultimately, that it can trust me to do it.
I then move the dog's lips and check its mouth and teeth. I lift its feet and touch its tail. I do this gently, and I praise the puppy or dog for being patient and compliant. Afterward, we have a lively play session.
It is as simple as that. No bribing, no distracting - just building the bond and making sure the dog understands that these procedures are an inseparable part of our life together.
If you only handle this kind of interaction when it becomes necessary, you will see resistance. That resistance leads to your dog setting boundaries, and to you backing off, because no one wants to get bitten.
2. Structure: you believe the dog gets an opinion on what you touch and what you do not touch.
As much as you want to believe that dogs deserve freedom of choice, there are limits to this freedom, and those limits are essential to a functioning life together.
A dog can choose whether it prefers a ball or a stick. It does not get to choose whether grooming or medication routines happen, because having this type of agency implies that an individual who exercises their power of choice understands the repercussions of their decisions.
Dogs do not understand the repercussions of not taking medications on time or of not adhering to grooming routines. Therefore, they do not get to exercise agency or have an opinion on these matters. Any attempt by the dog to express such an opinion - through avoidance, snapping, growling, or biting - should be discouraged and corrected, and the routine has to continue as planned.
3. Surface: you cannot administer medication, cut nails, brush your dog, or do any necessary handling, and it will get worse the longer your dog is allowed to impose restrictions on you.
If your dog decides you should not touch its feet, and you accept that, you are in for a lot more trouble. Left unaddressed, this expands. A dog that believes it controls these interactions may decide it can only be pet when it wants, and only for as long as it wants.
This can look like a dog coming over for a belly scratch, tolerating fourteen seconds of it, and then snapping at you for being too slow, scratching too long, or leaning in too close. The same restriction spreads to the face, the tail - wherever the dog decides to draw the next line.
If you recognized your dog in any of this, stop and look at the bigger picture.
Do not back away because your dog does not like you touching its feet (or face, or tail). Let the dog know that not wanting it is not an option, and go back to doing what you were doing. Moreover, start doing it several times a day, until the resistance completely stops.
I always urge dog owners to keep things simple. Teaching a dog to accept manipulations with its body parts is, similarly, super simple. That is, neither of you gets to back off: you - from dealing with an opinionated dog fairly and appropriately, and a dog - from accepting what has to be done.