Baking is a fantastic idea - teaching kids essential cooking skills and getting them to help with measuring and mixing is a great way to occupy them, plus you get a tasty treat at the end!
For indoor activities during the colder months, I find board games a great option for some family fun and interaction. A few classics like Scrabble or Monopoly Jr require minimal set-up and pack away, and are great for a wide range of ages. Also think along the lines of jigsaws - they can be found with lots of pieces for older kids (and adults!) and are a good challenge.
I also love the idea of a 'treasure hunt' around the house. You can hide small toys or treats and give clues to keep the kids occupied and engaged, plus it's an excellent way to sneak in some problem-solving practice! Could even have themes, like finding different coloured items or objects beginning with certain letters.
For something a bit more relaxed, why not put on some music and have a dance party? Dress up, sing along - loads of fun and a good way to let off steam indoors! If the weather outside is gloomy, you could even set up a tent inside with fairy lights, or make dens with sheets and blankets. A nice cosy hideaway!
Kept my reply general so it could be useful for various ages, but would be great to hear specific ideas for different age groups too. Always looking for new inspiration!