Wow and here I thought someone was building an underground lab for ants in their backyard. Good thing no one beat me to it yet!
I'm sorry to hear about your predicament. First things first, your parents care about you and they obviously see ant-keeping as "not very important". You can't blame them and I hope you don't resent them for not sharing your fondness of ants. The best thing for you is to not give up so early. Persistency is a key characteristic of successful people. Why? You tell me.
Sit down, write down all the reasons you can think of for why keeping ants makes you happy and prepare a speech to give to your parents. Include everything you've learned and how it's made you a better person. "I saw the queen tending to her children and it reminded me of how much work you put in to raise me so I love you mom," may be your ticket out of this mess. It's important to be genuine, as it is with all things in life, so don't lie or try to fake anything. Just be honest. I'm sure keeping ants makes you happy, and your parents definitely want you to be happy even though they may decide things for you that don't seem very helpful. In their eyes ant keeping is just another worthless hobby you're going to get over in 2 months. Prove them wrong. Ask your parents if they have a minute to talk and make sure you listen more than you talk. Don't throw tantrums but use logic and persuasion to sway their opinion.
It's important to also bring to the table the things you can do for them. Sweeten the deal. Offer to do chores or extra studying. If your parents love to do gardening, offer to go out there and tend to their garden with them. Take part in the things your parents do in their free time and they will start recognizing your hobbies too. Take the opportunity to bond with the most special people in your life - they won't be here forever. Apologize for your mistakes and promise to be a better person from now.
If your parents are not lenient, show them that you can be responsible. Even though they may say no to your request at first, change your behavior immediately. Start cleaning your room without being asked to. Do the dishes after dinner without being asked. Drop off dirty laundry once they start to stink. Take care of all your responsibilities and try to add even more to your list. Don't just do things to get it over with quickly; take your time, be diligent and do it right the first time. Always thank your parents when they drive you somewhere, cook you food or do your laundry. Even though they may not change their mind, always be grateful for their presence in your life and the fact that you can indulge in the hobbies you like. "Gratitude is not only the greatest of virtues but the parent of all others."
After you sweeten them up with emotional arguments, switch to logical ones. Explain to them the science of insect barriers. Demonstrate your knowledge of ant anatomy by teaching them how ants climb vertical surfaces. Remember, the point is to prove that the ants cannot escape their enclosure. Your parents believe they will escape and that's the entire reason why you're in this mess. If you can't persuade them, offer to use a different design for the enclosure. One with a proper lid and fine mesh for ventilation. If they counter with the fact that the ants will be fine in the basement, you can explain to them how heat stimulates the metabolism of ectotherms and the lack of it will stunt the growth of your colony. Research the facts and prepare a well-thought out argument. In the end, your ultimate happiness depends on your ant colony not only surviving, but thriving. If they are barely scraping by, freezing and neglected and left to their own devices in a basement, it would do you shame not only as a caregiver but also as a person. They are your responsibility, and just like any other pet, it is up to you to care for them to the best of your ability. It's true that your colony isn't going to grow as fast in a temperature range below 70 degrees F compared to higher than that.
I have no experience with hibernating ants so I will leave that question up to the others to answer. However I did want to present you a way to convince your parents to let you keep the ants in your room. Everything I said will work not only for that purpose, but also for other things in life and work. Honesty, diligence, gratitude, etc. The ants will come and go but the quality of your character will remain golden or as rusty as you let it.
