Another opinion....IME firewood cures faster left uncovered and exposed to wind and sun. IMO A tarp cover to keep rain/snow out, also keeps moisture in. It would not be a surprise to me that a stack of green wood that is covered takes a very long time to cure.
Maybe the ideal situation would be only cover the stack to be cured when it is going to rain/snow!
On the other hand, if you have a stack of already well cured wood that you'll be wanting to burn that season, go ahead and cover it to keep the rain and snow off.