You clearly recognised that the car park had not been gritted/treated and that there were icy conditions.
Therefore, you surely should have driven accordingly.
You did not, so your fault.
No doubt you will put in a claim and try and add something to it. That's why sensible drivers pay a premium on their insurance for - fools like you.
As I have stated, you recognised that the car park had not been treated, you recognised that it was icy and yet you basically drove into a post.
I rest my case.
How some people come to obtain a driving licence is beyond me.