Or another somewhat different method:
snowmanexpB.moho
In this case, the snowman is left on the same layer, and a little tweaking of the bone strength gets it to move pretty well. The snowmans top button jiggles a little bit with the head movement, but it's not too bad. My first thought was to go to the point binding, but I wanted to see what could be done without it. As in LM's example, bind the eye switch layer to the head bone. Also, because I wasn't using the Bind Points tool, I wanted to make sure that the arm bones didn't affect the points on the body. And thats a call for the Offset Bone tool.
As you can see, I moved the arms (in the Zero frame) away from the body by translating their layers, and then put bones in them (parented to the middle circle's bone in the snowman's body). Then use the Bone Offset tool to move the arm bones back to where they belong, and the arm layers follow along. What this does, apparently, is make Moho act as if the bone is still really far away from the other points in the character, so the bone doesn't have enough "strength" to affect them. Even though, looking at your screen, they appear to be working in the same spot. One of the cooler additions in the new version, I think. It can be a little wierd building your character looking like it's exploded all over the place when you are on the Zero frame (you can get a look at it proper on the Zero frame by selecting the Manipulate Bone tool), but you get used to it. It's the thing that makes all the automatic binding work, where I almost never used it in the previous version. Now I use point binding for only those things that really need it.
That said, I agree with LM that this is a place where point binding, as the file stands, is a very good, accurate option. Another, if you don't want any deformation of the shapes, would be to place each of the snowman's body sections onto a separate layer, and then bind each of those layers to a bone. You could select all the points for a particular section, and then just cut and paste them into a new vector layer. The shape information (colors, line widths, etc.) goes along with it.
Y'see, there are a lot of ways to get there from here in Moho. Don't let the options confuse you, it's good to know 'em all so you have the choice when you come up against a problem.
--Brian