I live in Vancouver so almost everyday is a rainy day here! Honestly? We go outside anyway every single day. Even just an hour can help with cabin fever. I put my daughter in a one-piece rain suit and rubber boots and we go looking for puddles. Then we get sticks and use them to splash the puddles. And when we can find them we get rocks to throw in the puddles. It's a blast. But then, I'm a big fan of the saying, "There's no bad weather, only bad clothing." Make sure you're dressed for it, too. Puddle jumping is way more fun if it's a family activity. I splurged on fantastic rain boots this year (worth it since I wear them all the time) and a good rain coat and winter is much more fun because of it.
For indoor activities we have a craft bag that we pull out on special days with feathers (we got a big bag of them at an art store) pom poms, and little pieces of paper (I cut up our Christmas wrapping paper into little pieces) and we glue them to paper or paper plates. If I'm feeling adventurous I'll break out the glitter. Cooking and baking is fun, too, if you have the ingredients on hand. My husband has built my daughter a few forts with blankets and pillows and that's been a big hit.
If it's still raining I hope that helps! When I moved here the gloomy, rainy days really got me down. Since I've learned to embrace them it's been so much better. Have fun!