The first benefit of the War Caster feat is (PHB, p. 170):
You have advantage on Constitution saving throws that you make to maintain your concentration on a spell when you take damage.
The spell sleet storm doesn't deal damage, but the game designers still wanted it to make characters in the AOE make a Con save to keep concentration. So the spell description states:
If a creature is concentrating in the spell's area, the creature must make a successful Constitution saving throw against your spell save DC or lose concentration.
Does the War Caster feat still give you advantage on a Constitution saving throw (to maintain concentration) made because of the sleet storm spell?
I definitely don't think this is an intended interaction, but RAW, War Caster seems useless for this situation, since it says "when you take damage", and sleet storm is not a damage-dealing spell (the Con save to maintain concentration due to the spell isn't due to damage).