In the past I used a plastic sled on public land, but I made sure to purchase the most rigid sled I could find, which I feel helps when dragging a carcass over logs or other obstacles.
They also make sleds designed for this purpose (
1,
2) that also provide some protection from debris getting in the carcass as they completely cover the deer. When considering the extra protection these products provide, that some have harness systems for hands-free dragging, and that some are light weight and compact for taking along on your trek into the woods, it makes the price tags a bit less unappealing.