I had a similar idea for keeping our front steps free from ice. This is a much smaller area than you are planning but even so I could not make it work. My idea was to pump water heated by our solar panels through pipes underneath the (wooden) steps. I had hoped that I could use relatively cool water available when the panels were not producing enough to contribute to hot water or space heating. In reality even if I use hot water at peak panel output it doesn't keep the steps clear of ice. It does help a little but not enough to be worth bothering with and I have given up on the idea. I haven't even tried it for the last few winters.
Of course you may be better at this than I am but I would not be optimistic that you can heat a large walkway using this approach unless you put an awful lot of energy into the system.
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