Explain to them that every activity in life comes with risk. You can be injured playing volley ball just as easy. You could be critically injured in a car accident going to the grocery store. Not only is it impossible to protect you with 100% certainty but it is morally wrong. You are a person and becoming an adult American citizen with freedom. If you are not allowed to start exercising freedom and taking responsibility for your freedom, how will you ever learn to function as a responsible adult?
Let them know what snowboarding means to you and how it fulfills you as a person. Let them know how being denied that fulfillment will create resentment toward them. Let them know all of the mental and physical benefits that you get from snowboarding and explain that the benefits far outweigh the potential risks which really statistically are far lower than many mundane activities. You are hundreds of times more likely to be killed or injured in a car than you ever are snowboarding. How do they propose to protect you from that; never ever let you drive or ride in a car again?
Let them know that you understand and even appreciate their desire to protect you but that the road to hell is paved with good intention. In their desire to do a good thing and protect you, they are causing far more harm to you at least psychologically. Let them know that you learned a lot from this and have an appreciation for slow, steady progression in and out of the park and that events like this actually make you a safer, more competent rider.
In the end though, the sad truth is as a kid under their roof, you don`t live in a democracy and you may have no choice other than to wait until out from under their control. Being able to accept unpleasant realities is a part of becoming a responsible adult. If they don`t give in, take it with grace and don't be a bitch to them about it. Quite possibly, they may relent if not this year, next season if they see that you handle it with grace and maturity. If you go apeshit, they will most likely dig their heels in and never relent. Argue your side rationally and with passion but in the end if you don't win, be mature and show them through you actions that they were wrong in their decision.
best of luck to you and whatever the outcome understand that you are young in in no time you will be free to make any decision you want as an adult. This too shall pass.....