We've
had good luck just leaving these low grade extension cords out year
round...that is until this year when one
of the deer deterrents kept
tripping a breaker when it rained.
A visual inspection will
usually show you where the damaged spot is. I think this one may have
been at the wrong end of a shovel or fence post.
This is my favorite thing about the farm/homestead lifestyle, the interest in repairing things instead of throwing them away and buying new.
It's a bit trickier, but did you consider doing an in-line splice? I've found that splicing cords that way is much neater and allows you to lie the cord flat.