There's lots of indoor games that children love to play. I'm a teacher so I have done things like:
Heads up, 7up
upset the fruit basket
basic excersizes with imaginitive names (reaching up can be touch the stars, touch your toes can be cherry picking, etc.)
Hope that helps! Have fun
A good exercise would be anything she likes that involves moving around -- as opposed to watching TV or being on the internet. If she's reading a book, I would cut her some slack, since reading benefits children in other ways.
Although I'm young, I'm kind of old fashioned and not a big fan of technology so my ideas are going to be all outdoor related!
When I was a kid, my favorite winter activity was playing outside in the snow. Before snow fell, I liked being outside waiting for snow to fall! We built snowmen, went tobaggoning, tried to build igloos but that never worked out because we don't have the right snow. We had snow ball fights and made snow angels. Walking in the snow is hard work. You could even teach her how to snow shoe - that is one of the hardest workouts in the world but lots of children love it.
If you have a mountain nearby, you can take your child tubing, teach him/her to ski, ect.
When it's just cold out, we liked to go for walks outside, stomping on the crystalized dirt. Kids generally aren't the same as adults when it comes to temperature. I used to even swim in the rivers during winter when I was young and never even felt the cold.
We especially liked playing with the dog outside - that probably burned enough calories for us to eat many portions of dinner.
Mind you, I grew up on a dairy farm and my parent's let my sister and I roam free! We had a lot of fun growing up and were always active.
We had superb imaginations. I remember this one time we created a fake boneyard out of sticks to scare away neighbors (weird kids, I guess lol)! We also went through a phase of having fun stick fights. Also, Four Square was our favorite sport to play, we'd walk for miles to find paved roads in order to scribe chalk squares and play with a ball. We also loved tether ball! All you need is a tree, a rope and a rubber ball.
If you don't live in a place where you have a yard, you can take your child to a park. Ice skating is always a fun winter activity!
We never had skates but we still had a lot of fun slipping around on the frozen ponds back on the farm. Fun days!
There are so many things to do in the cold seasons! Also, you can send your child on treasure hunts to find things to make christmas ornaments, like those really cool looking pine cones or holly or whatever else you could use! Again if you live in town, you can just drive to a park somewhere.
Adequate clothing makes all the difference in one's physical comfort level in cold weather. Layers are great, as they can be removed when body temp heats up.