The important thing is to find out and understand their specific concerns, then address those concerns.
There are many legitimate concerns of having a bunny in the house. I’ll give you an example concern and a possible resolution to it: Chewing through wires is one. y bunny, Porky, has caused a lot of damage to wires in our house that we didn’t think he could get at but did. Since I’m the adult responsible for buying new wires it’s OK for me to just decide it’s a cost I’m willing to take on. If your parents aren’t willing to risk the cost of bunny destruction, maybe you need to agree to pay a pet deposit to cover such costs. Many landlords require pet deposits from tenants to cover possible costs of damage caused by pets. If your rabbit doesn’t cause any damage, you will get your deposit back when you are old enough to move out.
Solutions need to be tailored to your parents exact concerns, just showing them how nice it can be to have a bunny inside doesn’t do anything to solve their concerns.
Don’t worry too much about it getting cold. Bunnies don’t mind that nearly as much as they mind really hot weather.