Depending on the kind of oven you buy, you could permanently leave a pizza oven outside.
Placing a solid brick oven or stone-encased model outside during the entire year should be acceptable if you're ready to clean it before use.
You should use a cover and shield it from the weather for other types, such as rolling-cart variants and portable outdoor pizza ovens.
The same care should be used with these more delicate designs with your preferred Grill or BBQ setup.