No, they may not tarnish either. Most of the landscape lights you buy will be pre-finished and coated with a clear protectant. Our copper lights have been outside for months without any damage at all, they are coated in a clear sealer by the manufacturer. If yours are (and they probably are) the most you should need to do is wipe them clean every so often. If they are not, over time they will darken and slowly turn green, the package should say if they aren’t. There are any number of commercial cleaners out there to clean the tarnish off, some very good home remedies too. If they do tarnish and you don’t like it, you can clean them and coat them with a clear sealer yourself so they don’t tarnish again. I like Minwax Satin Finish Acrylic Sealer, which you should be able to get at Home Depot, or Lowes.

copper can corrode but not rust, it will go green, flaky and pitted.