Yeah, we got drenched here on Monday... a cold, hard, all-day rain... but yesterday was sunny, windy and cool... my stacks are plenty dry again, as it's just surface moisture that evaporates near as fast as water on pavement. Heck, last night I pulled some off the top of one stack for a fire in the shop... it was plenty dry and burned just fine. Even rain-soaked firewood will dry really fast when moved in the house... especially during winter when relative humidity is low.
I'd never heard of coverin' (unseasoned) firewood before joinin' AS... never even seen it done?? Some people will move it into a shed after it's fully seasoned... like after two years or so. Me?? I just toss enough in the basement close to the furnace every fall to last all season... so yeah, I reckon that's like puttin' it in a shed just before heatin' season. Although it is a bit different because all off my firewood is kept pre-warmed at room temperature... or basement temperature.
Even in mid-winter, when the stacks get covered with snow and ice, a couple days of sunshine will usually clean them right off as the dark-colored wood soaks-up the solar heat. In the past, when I knew I'd be needin' to retrieve some wood from outside within a few days, I've laid some old planks on top just so I can flip any snow/ice off easily... but in reality, a little weather-watchin' and foreplannin' will eliminate even that.