YANBU.
Hmm ... everyone, (on here who is against you), seems to think a "small", (sugar-filled), treat is perfectly fine, and that any kid's life will be sad if they are not given treats "now and then".
But the questions are ... how much is "small", and how often is "now and then" ?
And is eating sugary stuff inbetween meals really a good idea anyway?
If there wasn't an obesity problem in the UK, it might not matter about these treats, (apart from any dental concerns), but there is an obesity problem and there is also growing evidence that sugar itself is bad for us.
I worry that a lot of parents don't see the problem with sugar, and/or are in a state of denial re the dangers.
The "healthy eating" message is being put out now, but very gingerly, as educators are still probably too scared to say "zero refined/processed sugars would be best" ... and a lot of them are overweight themselves.
Then there are the 'vested interests' who don't want a "zero sugar is best" line of thinking. (Such as the manufacturers/sellers of "sugar" & "sugary treats"!) They are the ones who want us to think that a little treat now and then is fine, even when they know we are actually having a big treat and/or having it too often!
Having unhealthy 'treats' when kids are thin/active, (ie "runnning it off") is probably OK-ish, but it doesn't mean there won't be any long term consequences of growning up with a lot of sugar in the diet. (Eg the association of sweet things as a reward can be hard to kick in adulthood, when running it off starts to be more tricky!)
IMO, putting ice-cream vans inside parks is like putting all those sweets next to the check out lanes in supermarkets. (It's creates "pester power" & a temptation for parents to just give in for a quiet life/not to be seen as "miserable".)
Control over "treats" is hard at the best of times. And I don't think ice-cream vans in parks is going to help parents with young children make the right choices.