I'm not sure where you are, but here we have an early childhood and family resource center and they do a bunch of activities for kids and families for free. Maybe there's something similar in your area. Also there would be a cost but you could look into sports depending on your kids ages, we have the kids in Gymnastics and the programs are 10 weeks once a week. It's organized and cheaper than going to the trampoline park
Go to your local supermarket and get a handful of leaflets and cut out pics, make a collage of animals, food. Play restaurants with the food pics. Make a zoo with the animal ones. What do the animals eat? Where do they originally live etc. my son lives watching “Danny go” on YouTube. It’s a dancing show, gets them active. Have a “party” turn lights out, get dressed up, music on, dance about. Fashion show, get kids to pick some random clothes or if you have some spare, make some clothes, cutting old ones up and sweeping to glueing together. Bring me a…game. Say an object, hat, kids run and first to bring a hat wins, dinosaur, red pen etc. make an obstacle course. Make instruments and do singing. General crafts, baking etc.
Library or museums
Playdoh, arts and crafts, colouring, baking, puzzles make up games for home
How cold? We still wrap up and go to the park. The colder weather is actually really good for them if dressed well. Otherwise the library? Is free in the uk and they do children’s activities. We have great garden centres here that have lovely Christmas decorations with soft play areas - don’t know if USA have that? We also go to local ponds and feed the ducks or go and see the horses in the field near our house
Do you have recreation centers where you live?
Check local libraries. A lot have pretty regular playtime/storytimes for younger kids and even book clubs and craft events for older kids
We still get outside every day... no such thing as bad weather, just improper clothing. It was a high of 42F today & we were at the playground for a few hours with our friends. Friday it will be a high of 36 & my 6 & 9 year old will be at their outdoor nature class for 6 hours. Otherwise, we play (rotating toys helps a lot), read books, bake, do crafts, experiments, card & board games.
We do lots of crafts and stuff , baking , cake decorating, painting ornaments , Christmas card making ,I got a book that’s 24 crafts countdown to Christmas happy to send to you pics of pages for inspo. I picked up a couple orinment painting kits the other day for £1 each !