If it's just too cold and miserable outside, stay inside! You can always go to the International UFO Museum and Research Center and bring your dog too! Admission is super cheap and it's at least an hour of interesting information. That is, as long as you're at least entertained by the thought of aliens.
Remember when we said some natural places are just cooler in winter? Well, the Origami in the Garden shapes of Los Cerrillos look just as neat against the white contrast of winter as they do against the greens and reds of summer. Drive past, take pictures, and stay comfy in the warmth of your car.
Sometimes a change of scenery is all you need. Search the likes of Airbnb and other home rental sites for a truly unique place (with a view, a new yard to play in or sledding hill nearby, perhaps?). You can explore a new space outside, stay warm inside, and find lots of new places to play.