We didn't let any weather stop us. Just got thermal vests, a wool jumper and tights for each child, with very good waterproofs from Decathlon on top. And a dog. The trick is to always have a purpose for your walk. Collecting conkers for nature table. Finding five variety of leaves. Identifying birds etc. Woods are great in winter and the Woodland Trust has a great website full of ideas for dc.
And saved up for a course of horse-riding lessons which took place in an indoor arena when it was really foul outside. Not cheap but we got a course of eight or twelve each winter depending on what we could afford.
Depending on the age of your DC (usually around eight) you can start enrolling in individual sport classes they enjoy such as tennis, badminton, Pickle ball, etc and there are usually indoor versions of the training available during winter which is much cheaper than DL gym membership.
Then have set times for certain indoor pursuits. We tended to do crafts on winter Sunday afternoons. You can thrift materials from vintage or charity shops. And we worked our way through a children's cookery book on Saturday evenings.
Also You Tube evenings where you each choose a song to dance to in turn.
Large jigsaws on the go. Reading nook.
Ask grandparents to buy the shells of dolls houses, farm sets, garages, and then you fill them with home made or thrifted furniture, animals and figures.
Dressing up box. I sewed costumes such as a Japanese geisha, cowboy, red riding hood, mermaid, witch, doctor and nurse. Again thrifted a lot of the materials and those costumes lasted years and were played with a lot. Trick is to only bring out the box at certain times.
Lastly - always a winner - have the wherewithal to make a den when everyone is bored and snappy and the weather really isn't cooperating. Massive cardboard boxes with windows and doors drawn on when they are tiny. And for older children, old large double duvet covers (thrifted?), pegs, short lengths of string, old quilts, cushions, maybe a small stepladder. Make on an upstairs landing or roof space.