A dry, cool place is all you need for winter pool chemical storage.
It’s not complicated. A garage or shed that stays above freezing works fine. Keep them off the concrete floor (use a shelf) and away from anything flammable or metallic.
Moisture is the enemy. Lids tight, containers upright, and never mix chemicals together even for storage. If your garage gets humid, a plastic tote with a lid adds a layer of protection.
Don’t leave them outside. Rain, snow melt, and direct sunlight will ruin them fast. Inside the house is overkill unless you live in a igloo.
Your pool will thank you in spring.