If you're seeking an enclosed structure for your greenhouse that can withstand wind, rain and cold, but also can be built cjeaply, consider a geodesic dome.
Geodesic dome structures are cheaper and easier to build than you think. Domes are some of the earliest man-made structures ever discovered. Paleontologists have unearthed domes built from Mastodon tusks.
No fossils are required to build this dome -- some readily available scrap electrical conduit will do perfectly. You can construct a geodesic dome with a series of triangles built from straight material. The more triangles you use, the tighter curve you can achieve. Here are some great dome calculators that can help you determine how many triangles you'll need to make based on your desired dome size.
After you've cut your conduit, the ends must be crimped using a bench vice or hammer. The final step to prepare your pieces is to drill holes in each end, preferably with a drill press, but a drill will also work.
To enclose your dome, you can use greenhouse plastic, or construction plastic which is much cheaper and almost as durable. HomeFixated has a great guide with more details below, so check it out if you're interested in putting one together.
Building a Geodesic Dome Greenhouse for Under $200 [HomeFixated]