But the other mother wasn't trying to protect her child from the elements
. As I say, I have no issue with you asking for a reconsideration, but it isn't fair to say that her child having 'GDD' was part of the issue, when your child had 'DS, heart condition, lung problems...etc, etc.' Family fund isn't about assessing the child's SN for worthiness, DLA does that.
GDD is, IMO, an awful, awful 'label' to have. It makes everything the child struggles with sound trivial and minor, implying that the child will catch up. It just isn't so.
GDD is my DD's 'label' (amongst others) - she is at special school. There are many, many children with DS, who are able to cope with MS school. I have a friend with a child who has 'GDD'. He is 5 and can't sit unsupported, walk at all without support under the armpits, speak, control his arms or hands, etc. He is still deemed to have 'GDD', because they can't find another label to replace it with 
As I say. Nothing against you asking for more - I think I would also do so, the likelihood is that the person awarding didn't realise that Mac Major accessories are £££ and thought 'footmuff', £50 should do it.
But please don't trivialise GDD.