I just want to say that we need more people like you. I get that being this active is not for everyone, but damn, we need it right now. And I'm including myself in that statement.
You're not wrong, but I also think it really depends on where you are. It can get too cold for dogs in October in some places. In Colorado mountains, it's averages of 20s Fahrenheit (slightly below zero Celsius). I wouldn't keep my dog out in that weather for long. Unless it's a badger.
Trans kids have to be some of the strongest people I know. Like you said, they are already at a rough time in their lives just from being teens, and to add dysphoria, bullying and bigotry on top of that.. it's just so much shit.
It's terrible that you kid's friend's parents aren't supportive. He is lucky to have adults in his life like you who offer a safe haven. Based on what I've seen in my clients, having just one supportive person can create a resource that you can use your whole life.
Thank you for your bravery. This needed to be said.