Canines have very tough feet think about snow dogs, foxes wolves etc. They have special blood vessels that keep footpads just above the freezing point this is why it is important for the likes of me to trim the fur close to the pads under the feet of my lot in winter to stop ice balls from getting trapped and therefore making it easier for the blood vessels to exchange heat into the pads themselves rather than the heat being wasted in trying to melt trapped ice balls.
Dogs curl up for a reason the snow dogs for example will curl up with their tails around their noses and feet so that the warm air exhaled by their lungs will keep the feet warm.
Many modern domestic dogs have very little hair on their feet but they have adapted their inheritance from their ancestors and have fatty pads with real tough skin. These pads are comprised of fat (those of you that have had to deal with badly cut pads will be aware of the pale colour of the flesh this is the fat content) and thick tissue they act as both shock absorbers to protect foot bones and they help to keep out the cold especially the carpal pad the biggy on the back of dogs' front legs - a couple inches up from the foot, the skin over the foot pads is the toughest on the dog's entire body.
When dogs normal body temperature (101.5 degrees to 102.5 degrees) drops due to cold they shiver to increase muscle activity but and this is the real clever bit they also withdraw some of their circulation from the extremities to the internal organs and the veins and blood vessels as mentioned above have heat exchangers - carrying cold blood back from the feet to the heart this passes right next to arteries goes through the heart where it increases in temperature then carries the warm oxygenated blood back to the feet.
Therefore (nearly finished folk but I find feet fascinating so hope you not too bored yet) feet are supplied with oxygen and nutrients in cooler blood than the rest of the body uses hence cool feet
Also the feet will operate at lower temperatures because the fat is very different from the rest of the body's fat it has a higher melting point and a lower freezing point hence again why dogs have cold feet And what is more
.the same principle works backwards in the hot summer months and helps stop the body from overheating - now isnt that clever - i have 'coolthefeet' on cue - they stand in cool water - puddles etc in the summer when it's hot - this way i can cool their whole bodies down

This is why dogs dont need boots to keep the feet warm
As long as the pads are not cracked or spongy or showing any odd signs of ill health - your wee lad is fine
good question mechi - thank you