I want to keep the tree kind of short. I want it to look like a mushroom on top, then in the summer just trim the bottom.
Is this possible?
The comment by kevinsky is right on. Willows are fast growers, and even in our cool climate (Alberta) will do 3-4 feet a year. You would be constantly pruning.
You may be able to find a top graft, where a willow such as Dwarf Arctic Blue (S. purpurea 'nana') is grafted to a tree form trunk. This would reduce seriously the amount of top pruning required. But since it has full sized roots, I'd expect a lot of suckering.
There are many top grafted trees that may suit you better.
Look for a top grafted tri-colour willow. The top 'ball' will be about 5 feet across. they are usually centered 5-6 feet off the ground.