Hot tub shelter
You can choose from many alternatives to a hot tub gazebo. A wooden gazebo is very expensive not only when you purchase it, but also when you maintain it.
You can purchase an overhead canopy for as low as $40.
Outdoor porch conversion
You can try converting the outdoor porch into a hot tub room. This may seem expensive, but it will last a very long time and add value to the house. It will also let you use the hot tub in cold, rainy and snowy weather.
Hot tub enclosure
You can purchase a hot tub enclosure kit, designed to fit the exact hot tub model that you have. It can be built in just around an hour.