If you suspect your dog has ingested anti-freeze, call your veterinarian immediately. There is a new anti-freeze on the market made from propylene glycol that appears to be safer. The best bet is to carefully cap all containers of anti-freeze and keep them out of the reach of pets. My dog and I go for as many walks in the winter as we do the rest of the year. Lately, I've noticed that my dog's paw pads are cracked and sore.
Salt used for de-icing roads and sidewalks is the most likely culprit.
It dries out your dog's pads leading to the problems you've described. He goes crazy trying to chew them off. Keep the hair between your dog's toes and pads clipped short, even with the bottom of the foot. When hair is left too long, snow sticks to it, forming ice balls that are uncomfortable and hard to remove. Long hair between the pads also reduces traction, making it easier for your dog to slip and hurt himself on the ice.