Being thin doesn't mean it's not meant for snowboarding. I'd say not having a powder skirt is more indicative of that.
It's a shell. It's meant to be thin. It won't be warm on it's own with the exception of being able to cut out the wind. You need to add layers. Depending on size you can fit 3 shirts under it or a hoody or whatever.
However, I would suggest against all of that if any of it is cotton. Go synthetic.
And what you layer doesn't need to zip in to the liner. Unless you really need to have it as one when you take it off.