Yes, energy can be stored long enough in batteries to provide enough power for the winter, though it would be very expensive, use a lot of space and require inverters for AC power. Take a look at lead crystal batteries.
"Or should the energy be converted to hydrogen to be used as a fuel"
Well... if you don't mind using an explosive gas as a fuel, think about possible gas leaks... hydrogen in automotive vehicles are usually compressed to about 300 bar as well, so you would need to use energy to produce and compress it. Also transporting highly compressed gas is always dangerous, especially in vehicles.
Please elaborate on your question by adding the amount of power needed in the winter and for what purpose? I.e heating, cooking, lighting, transport or general use electricity. How much you can produce and how it would be produced also plays a factor.