If the farrier meant his feet are striped... Other breeds can display that as well.
As far as Paint/Pinto... Paint is a breed, Pinto is the coloring. Other breeds with Paint markings register as "Pinto" with the appropriate breed (Half Arab, TWHA, ASHA etc.) they can also be registered in the Pinto association (yup, there is one). Some breed registries are now also accepting the genetic pattern descriptor as well as or instead of Pinto (Tobiano, Overo, Splash White, Sabino White etc. )
This horse here looks pretty QH to me, and grey could be behind his odd spots as greys do sometimes get them, even if there is no Appy blood.