Some dogs do become less active in the winter and prefer to stay inside and be lazy while other dogs are more active and happy in the winter.
Just like people some people hate winter while other people love winter.
I have one dog that is more active in winter and he loves it while the other smaller dog hates winter or at least seems to hate winter and becomes less active in the winter.
Winter does tend to make some dogs more lazy than others.
I have 2 dogs a big yellow lab and a small poodle dog and during the winter the yellow lab seems to be more active and wants to run around outside more during the cold winter weather.
The yellow lab also loves snow and loves sliding around on the ice and has a lot of fun trying to pull me down on the ice as well.
I can make snowballs and throw snowballs at the yellow lab and he'll usually catch them in his mouth and he loves that game we play.
The poodle is more lazy though and prefers to stay inside the house more often and hates the cold weather but the yellow lab has a lot of fun out in the cold and also loves to lay on the porch in the cold or even go out and lay in the back yard in the snow.
So it can depend on the dog but some dogs do become lazy in the winter while other dogs may become more active.
Some dogs love winter and cold weather while some dogs hate it.