Eris is okay with this nit, but would like to point out that pretty much EVERY animal with feet has more sensitive skin on the top of the foot than the bottom. There are good reasons why you’d want to walk comfortably on uneven or just plain hard ground, but very few reasons why you’d want to be able to tolerate discomfort on the top of your feet.
My point was that dog’s feet are built to allow them to run for long periods of time over rough terrain. This toughness, if combined with the numbing effect of cold, can allow dogs to injure their feet without realizing the extent of the damage.
And my sister’s dumb dog likes to have people play with her paws. So maybe your dog is just weird. 