Your snowmen are beautiful!
I recommend Tsukineko ink. You don't have to buy a whole set. You can buy just 1 bottle of ink if you like - maybe the Cherry Pink or the Red Delicious. A little goes a long way. I have been using the same set for about 10 years.
I have tinted the complexions of people in several quilts with these inks. Works beautifully.
I would put a drop or two of the ink in a little water and apply it to some dampened white cotton cloth with a Fantistix coloring tool or a watercolor brush, to test first. It will blend better if you apply it to damp fabric. Then heat set with an iron. Start out light. You can always apply it again a second time if you want more color.
For my projects, if I decide I want a different color, or it is too dark, I just rinse the color out, let it dry and start over. This assumes I haven't heat set it yet.
I would use a small iron, like the little Clover iron, and just press the inked area - so you don't flatten your beautiful applique.
I love to try different mediums on fabrics. I paint fabric with fabric paints, Procion dyes, Shiva Paintsticks, the Necololor II watercolor crayons, fabric markers, etc. I think the Tsukineko inks would be the best way to go with your gorgeous snowmen.
Judy