hello. I'm more in town and only know Warmington as the pretty village at the bottom of the hill...I can see you getting snowed in quite regularly!
all the groups on the other thread still exist - rugrats and halfpints etc though Whizz Kidz is under new management and now called ikidz or something like that. its by the train station. so far the only comments I've had is that it is expensive for what it is.
Burton dassett country park is fab for dogs and kiddies. Take a kite to fly. Its a bit of a drive from you but most dog walkers go there.
Theres lots of lovely parks in the villages - farnborough, shotteswell are two on your side of town. Spiceball Park and Peoples Park in banbury town are both good. Peoples Park for the playground and birds, spiceball for walks and the canal.
The national herb centre and the falconary place are also places that you can take the dog.
Find the childrens centres as a first port of call - britannia road is the centre of town one. They will have a wealth of knowledge you can tap into.
There's a well recommended pre-school in north newington. but I think you will find that warmington will have one. Farnborough also has one.
Further afield take the children to hatton country world near warwick (its about 10mins from J15 M40) - they will love it. If you've managed to unpack then a trip to see santa there would be lovely. They also have a very good annual pass system. We used it alot when we had two pre-schoolers.
hope the move goes well.