Car batteries are designed to last between 4-5 years before showing signs of losing charge. The fact you got 10 years out of your last one is very impressive. You don't say how old your car's battery is, but the manufacturer's warranty is unlikely to cover it beyond the first 12 months of ownership. I imagine the combination of reduced mileage and the harsh winter has caused stress to the battery's components and caused it to fail.

The battery itself may have a warranty (if it does it'll be written on the top of the battery itself). Otherwise, you will have no other option but to purchase a replacement.