I still walk Jackson in the cold weather but his exercise definitely decreases during the Winter. I saw a tip on here in another thread that someone would throw a treat down the stairs, and the dog would go get it, going up and down the stairs! I thought it was a great idea. I also play fetch with Jackson indoors and he runs from one end of the house to the other, back and forth, fetching until he's tired out.
Doggie clothing comes in an array of different things, they even have little booties, really warm coats, etc. I'd look into it
As for the food, is your dog eating out of a dog bowl or a plate? Try a dog bowl. Some dogs won't eat off of plastic bowls, but they will glass or vice versa. You don't want your dog eating off the floor.
And dogs can't catch human colds as far as I know.