Here is my view,, and reason/explanation.
If you place the wood chips
into run now,,,, consider that the chips will not form a smooth surface. When the chips freeze the surface for the chickens will be somewhat irregular with protruding chips,,,, that can potentially cut your chickens' feet bottoms.
Had you placed a layer of chips a couple months ago,,, then that would have gotten somewhat flattened out , from chicken traffic. The chips would have settled, and not many protruding chips to cause possible injury.
Consider getting a bale of straw, and spread on top of sand. You can also add more straw during winter,,,,, when snow is somewhat only thing there. Straw will keep chickens' feet more insulated from cold snow ground. Straw also tends to remain dry by its own nature,,,, VS hay.
In the spring when snow, and cold are past,,, you can choose to rake out straw,, and fresh rake the sand . Add more if you think is necessary.
Post some pictures of your run, so we can get possible other ideas. Size of run also may factor into what would be best. If straw is available to you reasonably priced... consider keeping a couple bales unopened inside run. This way chickens can hop on a bale height surface. Those surfaces would also be generally dry. If snow covered,,, just turn bale to expose snow free side.
WISHING YOU BEST,,,,,,,,,,,,,,,,,,,,,,,,,,,,
