This page described "structures" used to support astrophotography. Large observatories use custom "domes" that can be rotated and opened. Moving the astronomical equipment generally means a lengthy teardown, setup, and alignment procedure being repeated. For smaller equipment, this teardown/setup is generally under 30 minutes, and the alignment procedure can also be between 15-60 minutes (it depends how far off the initial alignment "guess" is, how well the equipment is "behaving", and the overall experience in doing alignment with the equipment involved).
The most basic domes start at around $6000. The main benefit of domes is being resistant (insulated) to insects and winds, and in general allowing the equipment to be stored in the same spot during the day time without being exposed to the sun or other extreme weather (i.e. keeping dust/dirt away from the equipment). Domes can also be air conditioned and operated remotely.
Less expensive options are basically tents with cut outs. Or a "sky box" that uses a material similar to vinyl (or like the blue plastic convering used on swimming pools, or tarps). A "sky box" is open on the top, giving a telescope full view of the sky and ability to pivot/rotate within. During the day time, the equipment is just covered with blankets or other suitable layers.
Other options include sheds with roofs that can be easily removed or opened.
Finally, another option is a thick covering that is wind, rain, and basically weather resistant. The most popular for telescopes is TeleGizmos covers.
Custom 10x10x6' tall wind blocker (SkyBox: POC John Love
wd5ikx AT juno.com )
ThinkingOutside Smart Shed 5x7 (removable roof by 4-6 plastic screws)