Reference for Isobel's gear. Addition of blue mithril chain mail over upper torso is only real difference from normal smithing wear. Made to be practical, as well as protective.
Undershirt (not seen)
Light, fur-lined coat
Short leather tunic usable for smithing
Chainmail torso-cover for vital organs
Leather sleeves (based on leather sleeves worn by Brann Stark in Game of Thrones)