Are dog boots worth it?

I want to preface this by saying I am not just some overbearing pet own who does not want mr. Fluffykin's feetsies to get cold I understand that dogs are hearty creatures and do well in cold it is not the cold that is the problem it's the salt I walk my beagle even when it's cold because he is overweight and needs the exercise, but recently it snowed and people put down salt. Unfortunately this salt gets in his paws and even when I try to wipe it away or wash it out with snow, we rarely walk for more than a minute before I have to carry him back home because he starts limping with usually three out of his four paws. I cannot walk him anywhere else, and I don't want to stop walking him during the winter, but I know he would hate boots. Is there anything else I could do or are boots worth it?