I managed a storage facility for 3 years. We had some very well maintained buildings and I was fanatical about pest control. Still ..... I have seen what furniture looks like (and smells like) after being in storage (even good storage) for even a few months. You'll be sadly disappointed.
If you can not even consider selling your extra, or giving it to some one needy, then at least invest in some zip-up plastic covers that will encase the entire piece of furniture. You can check with local storage facilities for these. There is also a product available that you can put in the bags to help keep away moisture, though at the moment the name of it escapes me. Again, check with a reputable storage facility for this. Buy flannel backed plastic table cloths to cover the floor under your furniture, and throw over the tops of the furniture. This helps with condensation from the floor, as well as any condensation that may drip from the ceiling. If the building has a metal roof, condensation will be a problem in the spring and fall because day time and night time temperatures vary so greatly.
There is very little you can do about mice, and other critters in an out building. (I, too, lived in the country and I know this to be fact.) Temperature extremes are going to play a factor in compromising the quality of your furniture, also.
Even with all these precautions, I can still tell you, that you will be very disappointed when you finally pull that furniture out of storage. I'm sorry. It would be so much better to sell or give it to someone who will get some use and enjoyment out of it, and buy new when and if you need it.