Keep top cover bit above the pile, put branches / small trees on top of wood pile so that whatever cover you put is lifted from the wood, air circulates under the covering, but snow does not make wood wet.
As many has said, keep wood off the ground, pallets are good, pallets on top of concrete blocks better, add tarpaulin to ground below those pallets and moisture from ground will not get to wood at all and no grass etc. grows under so air moves under the wood pile, which helps air to move from bottom of pile to top of pile as sun heats the pile, I guess English word is convection for that effect, gravity operated air movement, it is like having slow fan at bottom of pile to blow upwards. Concrete blocks help even there would be tarpaulin under on ground.
Here I face my woodpile south to west, sun helps with drying and I don't have cover during spring and when it does not rain during early to mid summer, when it rains I cover my wood... right, at autumn I don't take cover off, air starts to be so moist that wood is not drying any more and wood is covered until next spring and dry air.
I do keep sides uncovered of course so that air moves trough the pile and under the cover.
My place is in swamp, so drying firewood is sometimes bit of an challenge, for example birch that is 3ft long and stacked to very loosely, each layer 90 degrees different direction and 1-2ft between each split log, it tends to mold and even after a year, when I remove bark, it is wet under the bark, so it takes at least 2 years for those to dry up here.
Might dry faster if I take bark off completely, but it should dry when it is split and no new water has entered into wood, but not on my yard, despite the sun and wind.
In our climate, from March to June is usually best drying season, other times it is bit hopeless to get wood dry, so I try to get best of this time frame, ideally I should have all firewood made by beginning of March, but in practice there is so much to do that I chop wood year around.
Old guys say, that you should have at least two years worth of seasoned firewood all the time and you make wood for 3rd and 4th year in a future, not sure how true this is for where you live, our climate is unpredictable, we can have very cold winters or winters without much chill at all, so better have extra firewood for that cold spell.
Hopefully some of this has some use for you, different wood, climate etc. of course requires different approaches. If we all could just season our firewood in Death Valley, seasoning would be not an issue
