Is it ok to have a wooden partition wall?

We'd like to build a wall in a food storage area to separate food storage and non-food storage. Are we able to build this wall out of OSB and leave the exposed wood as long as it's in good condition. Food grade storage would be ambient temperature and dry.

Nope--you cannot clean it

Paint it or cover the wood 

Agreed with above, wood is not a suitable material for food processing environments because it cannot be cleaned and is prone to wear/damage. I would look into PVC wall panels, these are easy to install and are a cleanable surface. 

As this is only a storage/warehouse area, washability is not critical.  No plant I've ever worked in is wet washing their storage warehouse walls.  But untreated wood will standout and attract questions, not to mention any gaps between the OSB could lead to potential pest harborage within the stud frame.  I mean, plenty of room for arguing it as most of us place sealed cases of product directly onto a wooden pallet with maybe a slipsheet, but I digress...

First plant I ever worked in had unpainted taped sheetrock as their warehouse walls, along with exposed concrete where the walls made up the outside of the tilt up warehouse building.  We had it on the schedule to sweep these walls to prevent dust accumulation once per quarter, literally just sending a guy up in a scissor lift with a big dust mop.  Auditors never had an issue with it.

Well, hold on there just one second missy!

OSB even in super dry conditions has an uncanny ability to shed strands of material as the adhesive in the facing dries out.

I rule NO.

We frame the wall up with wood then cover it with metal. The metal is ribbed like roofing metal. Easy to clean and fairly inexpensive.