Hope this helps,
Go to the little dropdown arrow next to the snap tool(The magnet icon) and make sure you have these exact settings:
These settings worked fine for me.
Some more things you should keep in mind:
- The offset of your solidify modifier should be +1 i.e. the thickness should come towards the outside
The icing and the donut should have uniform scale i.e it should have scale of 1 on X, Y and Z axis. If they don't have a uniform scale then you can make it uniform by going to object mode - > Press Ctrl + A and applying the scale.
You have to be in edit mode to move the vertices and change the shape of icing.
Snapping has a limit, you can't drag the icing too far and expect to have no intersections between the donut and icing(In ur case it should work fine)