It won't help in the same way now, because the excess fabric is already inside your appliques.
The snowflakes will probably lie flat if you are willing to quilt over them. In my experience, dense quilting will flatten a "puffy" area.
With the snowman and the hat, you *may* be able to spread some of the excess fabric to the outside of the applique areas. This would require smoothing the fabric towards the background as you sew around the applique -- not an easy thing to do. In my experience, it would be better to add quilting to the appliques to flatten them out. You could use matching thread to quilt straight lines in the hat, for example, and white thread to quilt swirls in the snowman. This would add a textural element too.