Wood for wall.

Must be something you could look up for codes in your community. I wanted the same thing to have more closet space and my carpenter told me that I would need all sorts of building code sign offs in our community so it's on hold for now.

Have you checked your local building codes? That is where I would start. See if this helps.

https://www.todayshomeowner.com/video/how-to-build-a-non-load-bearing-interior-wall/

http://www.sawdustinmysocks.com/2012/10/building-stud-wall-step-by-step.html

No building code will allow 2X3 for walls. Check yours out before starting anything.

Legally yes you probably need permit to do this, but with that being said it won’t be the first home improvement that got done without a permit! Long as it’s not a load bearing wall you can add a wall out of any size material you want. 2x2, 2x3, 2x4, your choice! It’s not doing anything but dividing a area and in a worse case senereo it could always be removed if it was a issue if you were to sale your home! Even then only if it was caught that it wasn’t a original part of the home to begin with!

I did this in my basement rec room. I built divider walls to create a living area and bedroom area with closet out of one large room. All 2x3 framing, non load bearing. Cheaper than 2x4s, and worked out just fine.

Gale Allen is correct. Build away!