depends ...
If it is a self-blanching type ... it should be ready to pick now - we have been digging it up for the last couple of weeks (we are in Berks). Frost will kill it off. Sticks will freeze fine for subsequent use in soups, stews, etc but not for eating raw.
If it is a trench type then it will happily stand outdoors until you need it. Officially it will last until the end of the year or end of Jan depending on the variety.