How do I protect my mini-doxies feetsies?

My one year old mini-doxie Oliver just experience his first snow fall. He loves to play and frolic in it but after just a few minutes he starts crying in pain and limping. I check his paws and he gets snow tightly packed in between his pads and it's so cold it hurts him (I'm uming). So I tried to get him little booties, but when I try to take him outside, he won't leave the porch and he'll either end up pottying in the house, or right on the porch. He just hates to have those booties on. We also tried clearing a patch of snow for him in the yard to potty on, but he totally ignores it, and we still can't take him for a walk. Since we live in the country, we have to walk through the snow for my little man to get his exercise. What should I do?