I don’t use anything on my droppings board. It’s the top of a built-in brooder and just a piece of plywood. To scrape it I use a garden hoe with a broken handle so it’s short enough to use in that tight space without breaking a window to break it loose, then a squeegee to rake the poop into a plastic bin. This doesn’t get every stain off but it does keep it cleaned off enough that there is no smell. This way I get pure poop for the compost pile, not something with a lot of filler. I’m not sure this would work with yours because yours is a tray, not a flat surface.
How often I need to scrape mine depends on the number of chickens I have and how humid the weather is. With a lot of chickens and humid weather I may need to scrape it once a week or so, but with fewer chickens and drier weather I can often go three weeks with no smell.
I don’t understand why that sand is still wet enough to freeze solid, especially since you have been stirring it to rake the poop out. I think that may be your problem, not the material you are using in the tray. What you are doing should work. Is rain somehow getting in to wet it? Is your ambient humidity so high it can’t dry out? Do you have sufficient ventilation? Is it truly sand or is there something mixed in it to hold moisture? I think I’d approach your problem from the aspect of the wet sand as opposed to the media you are using.