on most kinds of natural surfaces? no

horse shoes are for damp country and pavement, otherwise their hoof rots or wears out really fast, their hoof is basically a big thick piece of keratin like our fingernails, and domestic dog claws are not sharp because of the wear of pavement, whereas wild wolves mostly bite your throat out their claws are pretty dangerous too from natural wear on soil and plants that leaves a sharp edge on them

if you live in dry country like most of the central USA and never take your horse on the road it doesn't need horseshoes