Very nice @amblender
Did you try adding a force like wind to make the snow swirl around a little.
You could animate the location checkbox to turn on and off the affect, so it initially swirls like a real snow globe then reduce to then have the falling snow.
It would take some time playing with the settings to get it right though.
Also you can start the particle system for the snow earlier, like -20, so when the animation starts at frame 1 the globe is already full of snow, avoiding the first few frames of no or very little snow.
I’m not suggesting you go back and change anything.
Just my thoughts.
Its looking great as it is.