How to can carrots according to The Practical Produce Cookbook by Ray and Elsie Hoover.

Raw pack: Wash and peel carrots, Leave small carrots whole; slice or dice larger carrots. Fill jars tightly, leaving 1-inch headspace. Add 1 tsp. salt to quarts and 1/2 tsp. to pints. Cover with boiling water, leaving 1-inch headspace.
Hot pack: Prepare as for raw pack. Cover with boiling water; boil 5 minutes. Fill jars with hot carrots to within 1-inch of top. Add 1 tsp. salt to quarts and 1/2 tsp. to pints. Fill to within 1-inch of top with boiling cooking liquid.

Process in a pressure canner; pints 25 minutes and quarts 30 minutes. Process at 10 lb. of pressure if you live below 1000 feet about sea level. Process at 15 lb. of pressure if you live at or above 1000 feet above sea level.

How to freeze carrots:
Select tender, smaller carrots. Remove tops, wash and scrape. Slice lengthwise, crosswise or dice. Small carrots may be left whole. Water blanch cut carrots 2 minutes; small whole carrots 5 minutes.
Cool immediately in cold water; drain, package and freeze.