Thich Nhat Hahn is the only one I have read who attributes a significance to smiling. It may have to do with the challenging times he has had to endure.
The interview with him contains much of his practice, but here is an excerpt about smiling
We humans have lost the wisdom of genuinely resting and relaxing. We
worry too much. We don't allow our bodies to heal, and we don't allow
our minds and hearts to heal. Meditation can help us embrace our
worries, our fear, our anger; and that is very healing. We let our own
natural capacity of healing do the work.
Total relaxation is the secret to enjoying sitting meditation. I sit
with my spine upright, but not rigid; and I relax all the muscles in
my body. Breathing in, I bring my attention to one part of my body;
breathing out, I smile with gratitude and love to that part of my
body. For example, I breathe in and I bring my attention to my face.
On my face there are about 300 muscles, and whenever I get worried,
angry or sad, these 300 muscles harden, and anyone who looks at me can
see that I'm tense. But if while breathing in I can be aware of my
face, and breathing out I can smile to my face, then that tension
immediately dissipates. It's almost like a miracle. In just a few
breaths we can feel peace, happiness, and relaxation on our face. Our
face becomes light, fresh, like the kind of flower it was before.
Every face is a flower.
After breathing three or four times with "breathing in I am aware of
my face; breathing out I smile to my face," then I can breathe in and
bring my awareness to the muscles in my shoulders, because our
shoulder muscles are often tense. As I breathe out, I relax and smile
with my shoulders. Gradually we can move through the whole body, so
after just a few minutes we can already normalize our body so it feels
light and relaxed.
This is something everyone can do in the first minutes of sitting, and
not only when we are in the meditation hall. Wherever we sit, we can
sit beautifully, just like we are doing sitting meditation, and we
will feel stability and freedom. Sitting down to eat or do paperwork,
we sit upright and relaxed. Let us sit like the Buddha.