Hostas will typically die back when the weather begins to get cold; but, allowing the hosta foliage to remain into late fall and winter could attract pests and fungus that will damage them. The best way to keep your hostas healthy and disease-free is to cut back the foliage in fall. Hostas prefer climates with cold winters and warm summers, and are hardy through Zone 3. You won't have to worry about lifting these perennials -- they'll come back in full force each spring. And, they don't require dividing, but tolerate it if you'd like to transplant or share your multiplying hosta in the spring!