Storage question

I live in flats, and have access to a storage cupboard that is in the close (not in my flat). 

The cupboard will be pretty cold as there is no heating. 

Is it okay to put clothes into a plastic box and store in the cupboard without it getting any adverse affects? 

Don't want them to get mouldy etc. 

The door has a slight gap underneath it so air circulates in the cupboard, but I would plan to put the clothes into plastic boxes that I have. I just live in a tiny flat and like to keep it tidy and clutter free as much as possible. 

Thank you