I share the small cold storage room for storing potted figs with the family's other stuff that needs cold storage. I was ask "Why can't you put the pots horizontally on top of each other to take less room?"
I knew from the last one year experience that my pots never needed watering. I can stop falling of the soil when pot is in horizontal position by  thinking of some means.
What other negative things can happen to the plant itself, in biological terms or otherwise, if I store the potted plants horizontally in the dark cold room that stays under 8 deg C (45F) from December until end of March.

As long as 'somehow' they can be prevented from getting 'BONE-dry',
being either horizontal or vertical should not matter at all  (I think).
Some people do winter inground figs by pushing them FLAT with protection.
Try to maintain ~consistent temps between 20-40 *F for an overall healthy
 fig-dormancy; (and just plain moist).

I see no problem,vertical or Horizontal,it doesn't matter Just go for it.
I had it both way and it works fine both.
Best way to keep figs alive,better than any other place:garage,greenhouse,House,basement,etc.
Best Regards