A plastic tarp and pile of snow on the firewood has lost its charm, so I recently built a shelter for our firewood. It's most free-standing, so it can be removed if we need to.
I didn't want to spend $200+ to buy something nifty like corrugated plastic for the roof, so I used discarded materials from work - plastic coated printed Gatorboard ™.
If it leaks a little, it will be better than a tarp and easy to deal with.