One fun activity could be video games. If you have a console like a Wii, that's perfect for days when going outside would be too cold. The great thing about a Wii or its newer iteration the Wii U is that they have games where motion is the focus. Not to mention the systems are fairly kid friendly. Find a regular Wii online for cheap and a few games, and you can have a lot of fun for cheap.
One thing I've found that can keep one of my step kids busy are jigsaw puzzles. They are super fun, and give people a sense of accomplishment. Plus, you can get one that has thousands of pieces, and then put it together with the kids. You can see if you even like them by playing some online, but it's better to have the real deal which isn't expensive at most stores with a board game section.
The final idea I have for you is to teach your kids how to cook. Here is a great infographic on this and it can be a lot of fun for winter treats like cookies to whole meals everyone plays a part in.
1 - https://en.wikipedia.org/wiki/Wii_Remote
2 - http://www.jigzone.com/