I don't think you sound spoiled at all, I think you sound like someone that doesn't want her beloved dogs to have to be outside away from their family in the cold all the time.
You just have to keep pushing for what you believe in. Tell your parents how bad you feel for the dogs, and ask them to bring them inside more, for their welfare or for their love for you. And if it gets cold enough that the dogs might suffer, you must do anything within your power to help them, even threaten to call the ASPCA or do it.
I know it's hard when your parents don't understand your ethical stance. Mine didn't understand mine, and considered me a child when I was younger. They would tell me "It's just a dog." or ground me when I refused to eat meat, but I stayed strong, and now they respect me for my views, and I like to think I've altered some of there's as well. Just be persistent, show how much you care, and try to remain calm about it. And if the dogs are ever in actual danger, you may need to go above and beyond to save them.
But assuming it's just chilly, and not dangerous, take a stand, and continue to try and convince them. Ask them to spend a few hours outside with you without a coat. Be outside as much as you can. Prepare presentation, and be unflinching in your ethics. It isn't just your opinion that's hard for them; if they're like my parents they still aren't able to see you as your own person; but eventually they will if you remain strong. If you continue to show them how important is it you, and remain rational and level headed, they will see your convictions and likely respect them.
This is a wonderful time for you, you have become your own person independent from your parents, and what others want you to believe, and it will take time for them to respect that, but you will help discover yourself in the process, and find confidence in your beliefs and who you are.
You still feel you would be classified as 'spoiled' for believing something different than your parents, but that isn't the case. When you persist for what you believe in, especially if it's for the welfare of others, that is the most true and respectful thing; and you can continue to discover what you care about through following what feels right over what is easy. Good for you.
Please ignore Star, and Gallant Knight if he comments, and some of the other trolls of the boards. They search for any self consciousness, especially minors, or people who care about their pets, and just attacks. They always say anyone who lived with their parents must be a spoiled brat, which is insane, because you're supposed to be living with your parents at your age, and they did as well. Then they try and say you don't care about your pet or you would take them to a kill shelter, or something. It's nonsense. There is nothing whatsoever to make anyone think this young man or woman feels anything but love for her pets, and nothing to suggest she "whined" for the dogs. And in this generation, I've mostly seen uncaring parents, and teens and kids fighting for their pets welfare. Urgh, it's so ridiculous what people on the internet will say to get a reaction. Anyway, trust me, the trolls accuse everyone of all sorts of things, no matter how unfounded.