Three types of parsley may be grown in gardens: curly leaf, flat-leaf or Hamburg/tuberous parsley. They all are variant forms within the same plant species, and therefore tolerate the same growing conditions and ability to tolerate frosts and freezes. One notable difference among these three types is that the Hamburg or tuberous parsley overwinters better since the underground root survives a bit more cold than the fibrous-rooted curly and flat-leaf types.
Freezes occur when the temperature drops below 32 F, and widespread frost occurs everywhere in the landscape. Once it drops down to 29 F, frost occurs in both low lying and in slightly warmer, protected areas of the garden. An established parsley plant will show no ill effect from a freeze. A weakened or stressed plant from growing in overly dry soil conditions may abort weakest, driest leaves in the wake of subfreezing temperatures. Newly emerging seedlings or young transplants may also not fare as well from a first encounter with a freeze, but they likely survive.
Small parsley plants, including those in small nursery containers or just recently transplanted into the garden may benefit from some protection from freezes, although not necessary. A subfreezing night won't kill the small parsley plants, but it will stress them and require several days afterward for new leafy growth to continue. Relocate small containers of parsley into a wind-sheltered area off of the ground so they don't bear the brunt of the coldest surface-dwelling air. Plants already in the soil may be covered with an old bed sheet to trap the ground's warmth and lessen the effects of chill.
In regions with long, brutally cold winters -- such as U.S. Department of Agriculture planting zones 1 through 5 -- expect parsley plants to die once winter temperatures dip below minus 10 F, even with a protective snow cover. While early spring or late fall freezes won't kill parsley plants, extended exposure to temperatures that never get above freezing for months on end causes plants to dry out and die. Enjoy harvest of parsley late in fall or early winter in these areas with the expectation to plant new seedlings each spring.