Keeping your firewood dry is critical.  I’ve been through numerous tarps and had to replace them almost yearly until I started buying thicker tarps like this one:

Tarps will only keep the wood dry if it’s kept in place, so I use bungees like this to hold the tarp in place with weighted milk jugs:

Simply string a bungee through the milk jug handle and then to two eyelets of the tarp.  In the past I’ve used water in the milk jugs, but when frozen can crack the plastic and then drain on warmer days.  I’ve recently read about filling them with sand/dirt instead to avoid this problem.