I didn't originally do any stitching around the snowman or the appliques. I've now stitched around the snowflakes and finished with a circle in the middle of them. They are laying acceptably flat now. I also outlined around all the other motifs and it's looking better. As for the snowman, I may just stitch around the eyes, nose, and mouth and call it done.
I did learn quite a bit from all of you so thank you for all of the comments and suggestions.