Making up a whole picnic for all the kids was kind, and I can see that you've gone to a lot of extra effort in doing that.
Just my thoughts, and I really hope this doesn't come across harshly -
When my two were little, there were 4 of us who used to alternate each other's houses once a week, just for coffee/juice/biscuits. The DCs played with toys, and we chatted. It was very casual.
A new mum moved to the area with DCs of a similar age. She was lovely and friendly, and we invited her to join us.
Very quickly, despite our politely saying it was unnecessary, the new mum started preparing lunches for the mums and the DCs - beautiful food aplenty!
She also started laying on structured activities for the DCs, like crafts/painting/treasure hunts etc.
It was so kind of her, but it did rather tip the vibe of the group?
People felt that they had to reciprocate the effort level, and that just hadn't been the effort prior - so it eventually fizzled out unfortunately.
Op, why not just tip up to the park with snacks and drinks for your own DC?
In this weather, there's bound to be other parents there with their children.