Are the veg trugs painted or bare wood? If bare wood - maybe an application of clear deck seal.

If you go for a cover, make sure it is breathable - something like canvas, rather than plastic tarp. Or if you go for plastic tarp, make sure it isn't trailing on the ground or closed up all the way around the container. That will trap moisture and that would be counterproductive. Cover the top so rain and snow doesn't get at the trug - but open at the bottom so moisture isn't building up.

If the legs are sitting up on pavers, bricks, or concrete blocks that will help to protect them from ground moisture. Won't stop them getting covered up with snow but overall it will help with the longevity of the item.