I dont know if Doxie's have problems with their pads being sensitive. But, I would assume the would have it a little. Doxies especially smooth haired ones, are very sensitive to temperature. My April has to have a jacket when she goes outside in the cold.
I would suggest doing stuff in your home first. Like my doxie loves running around the house after her toys. She loves to fetch, so a lot of times you will find myself and my husband throwing toys or ice cubes to get her to exercise during the cold. Once it warms up, which won't be long, my husband and I will be walking every day after dinner and taking the dog with us.
I would suggest getting weight management food, I think Iams does one for overweight dogs. Plus, I would cut the treats completely, and I would cut out giving your doxie any "table" extras.
I hope it helps.