What can I use to make evaporating fake snow?
The phase transition you are talking about (solid to gas) is called sublimation. There are a few compounds that sublime at room temperature and atmospheric pressure, but the one I think would best suit your purpose is dry ice. If spread into the air as a fine powder, it could sublime before it even touches the ground, especially if the air is warm.

It's important to consider the safety aspects of this, though. $\ce{CO2}$ sublimes at -$78º\mathrm{C}$, so if too much of this powder lands on people, you could end up with some cases of frostbite. Additionally, you would need to keep this space well-ventilated since you will be significantly increasing the concentration of $\ce{CO2}$. I wouldn't imagine it would be too hard to meet these standards, though.