Good catch :)

I thought about this for awhile and the gap between harvest time for many crops and first frost isn’t enough to get more than a few inches of rainfall in most agricultural regions with favorable economics.

I think the wetness will wreck the insulation of the first meter or so, but won’t lead to much convective heat transfer if the outside never gets saturated. A big if, to be sure.

As an aside, it’s common practice to leave large piles of grain outside overwinter in the central USA and it’s not optimal, but they certainly don’t saturate the whole way through with water.