I also suffer from autism with adhd. This is not easy stuff to deal with, it is truly difficult. I just want to take a minute to validate your frustration. It’s very understandable for you to feel this way. I suggest you get a quality child behaviorist and set up a plan on how to address these issues. Make sure your husband is involved so you can keep the plan consistent-it won’t work if you don’t all keep it consistent.

I’m also a special Ed teacher, and I gotta say the threat of not being able to play in the snow is not a great motivator-though as a mom I can totes say I might have said the exact same thing in your position. There are ticks to learn how to stay focused, as an adhd cleaning a room is especially distracting task. Personally music helps me clean, as well as redirecting focus to the specific tasks at hand. Focus on positive outcomes and reinforcement not negatives. Negatives can lead to frustration while positives can lead to focus- things like “good job! But we gotta keep cleaning so you can make a snowman outside tomorrow!” Instead of “if you don’t clean you won’t get to make a snow man tomorrow” it can help to make some sort of list -visual as I’m sure he’s to young to read -like line up the toys he is supposed to clean up and use prompts like “great you finished the legos next it’s time to clean up the cars! Let’s work on that”
Honestly it’s a long road ahead - but a behaviorist for children may come up with a better plan.