You have to start with a plan. Define what you have in mind for the event (format, number of features, judging, prizes, etc.) set realistic goals, and obviously plan for features your hill already has, make it easy for them.
It's much much harder to get cash from sponsors than goods, so you should probably aim for some lift tickets, skis, gift cards, etc. as prizes, not $$.
Then go to your hill with that plan and see see if they're fine with the format and setting up all the features for you (including a tent for the judges, tables, chairs, audio, etc. I assume they have that type of furniture stashed somewhere), and possibly even participate in the prizes (free lift tickets, free burger or some shit like that). Also make sure you have logistical questions laid out so expectations are set from the beginning (will all participants need a lift ticket, or can they get to the course for free on the day of the event, liability issues, etc.) Make sure to include a marketing plan in there, how are you going to attract people to the event (probably social media and maybe a few posters around town, and ask if they're willing to help you advertise the event too)
Once you have their commitment it's up to you to make it happen by finding the sponsors and making it all come together. Basically once the hill has agree to setting everything up, the big piece will be finding prizes, so like people have said go to ski shops, skate shops, reach out to online retailers as well, they might be interested, restaurants, etc. basically any small business in the area might be willing to give you something in return for some exposure. And if some ski shops turn you down, you can also ask them for the contacts of some of their ski reps so you can reach out to these brands directly, worth a shot! If you can score a pair of skis you basically have your top prize.
Btw you should have zero problem getting monster or red bull on the hill to hand out free drinks, in my experience energy drink companies are always interested, they probably won't give you any money tho, but just having them hand out drinks helps with the atmosphere of the event. Same with having a food stand, if you can find a restaurant willing to set up shop for the event, that's always nice.
As for judges, if there are some somewhat notorious local skiers in your area I'd start there, (and use their reach to attract people too), and then maybe coaches if there's any at your hill, etc.
Lastly, see if you have some friends willing to help out, it can be a lot of things to juggle, so if you have some people you can delegate tasks to, it'll make it much easier for you.
Just a few top of mind things, I'm sure others will have more to share, good luck!
