If you "pick" as in "pick up" turnips you get edible turnip under the food category
If you use agriculture to "harvest" you get turnip under the plant category
The plant category needs to be threshed. IIRC this produces food type turnips and turnip seeds.
Seeds can then be planted on prepared soil, which can be made on on unfrozen ground by having a small fire burn out to leave the ash mark of "burned out fire"
edit: doh, that is unfrozen ground