Thanks for reaching out with your question. Carrots will grow in this region, so typically it's a matter of finding the right variety for your growing conditions and timing their planting to optimize growing conditions. There are five main types of carrots:

Chantenay type- 2 to 2 ½ inches in diameter at the shoulder and 5 to 6 inches long with a medium to large neck. Color is medium to light orange with a red core. Better for shallow, heavy soils than the long, skinny Imperator types.

Imperator type- the main, commercial, fresh-market type. They are 7 to 8 inches long with a top diameter of 1 ½ inches. Roots are deep orange in color with a lighter orange core. Roots become woody when fully mature, but are excellent when harvested at their prime.

Danvers type- conical with a top diameter of 2 to 2 ½ inches and length of up to 7 inches. Deep orange with a light center. Quality is excellent in young roots; becomes fibrous with age.

Nantes types- cylindrical with a blunt tip, 6 to 7 inches long and 1 ½ inches in diameter. Roots are bright orange with a small core. Tops are often small and require careful digging at harvest.

Miniature and Oxheart types: Baby carrots are sometimes termed Amsterdam types. The roots are 2 inches in diameter and only 2 to 3 inches long. Stump-rooted or round carrots are suitable for heavy, clay soil or container gardening.

In addition to finding the right type, starting them at the right time for a spring or a fall harvest is key. Carrots don't grow very well during hot weather, so you generally want soil temperatures to be cooler when starting a spring crop. In the spring they can be planted when the soil temperatures reach at least 45°F. For a fall crop, carrots are generally planted about 10 to 12 weeks before the first frost date. In either case they need full sun for at least 6 hours per day and preferably 8 to 10 hour. 

Can you describe the conditions where you are trying to grow the carrots (e.g., in ground or in a container/raised bed, what the soil is like, amount of sunlight)? That might help give some further insights into why your carrot plants are not producing well.