Strawberries will do ok outside through the winter. I planted mine out this time last year and thought that I had lost them because they seemed to disappear, but they came up in Spring and I got some lovely strawberries, but now if seemed to have doubled in number. I've replanted some in a raised bed, another lot down the side of the path and gave lots away. Personally, they are like a weed, they will keep coming back. Make sure your turkey doesn't escape and eat the strawberries
my daughter gave me 5 plants that she grew from her shooters from her plant. They now have shooters and I don't know whether to leave hen or plant them or cut them off. Her original has produced more fruit!!
If you don't want anymore, then cut off the runners and trim back the foilage, but don't cut the little leaves that will be coming up at the base of the mother plant, these are your next year's growth. Generally, just tidy them up for the winter.
My understanding is that strawberries only fruit well over two seasons and then the plants start to produce smaller and less fruit. So I have always grown a quantity of runners on so that the plants are never more than three years old.