Is There A Way To Shelter the Rock Climbing Machine?

Yup. This is what to do, make sure your move Objects are on, then just put a tiny room on your lot then repeat for a second floor, delete the 1st tiny room floor, shrink the 2nd tiny room floor to one grid, delete the walls but keep the one grid floor, click the round roof, adjust the size & length, click the clear glass roof style. Make sure to have your clear roof just above the climber machine.
Now you have a sheltered machine outside with an invisible roof.
PS: this also works with not in season plants.