Pack the mason jar full. I find each cone ("cake cup" / "wafer cone") takes a bit under 4oz, so this is a good amount for the four of us:

Then put it in the freezer and leave there until you want to bring ice cream somewhere. Also stock cones and sprinkles, have ice packs in the fridge, and some kind of small cooler.

This means you can go out on short notice: put ice packs and ice cream in the cooler, bring cones, sprinkles, paper towels, and a sturdy spoon, and you're set. At the park you fill the cones with the spoon, put on sprinkles, and enjoy!

When you come home and are putting things away, immediately fill up another mason jar and put it in the fridge for next time.