How you best deal with your carrots depends on your climate.
Blanch and freeze.
This is a good method if you have enough freezer space.
Dehydrate
I know it can be done, but I'd suggest to only do this if you plan on storing them very long term.
Canning
If you know how to do it, canning is an excellent method to store your carrots.
Storing in sand or soil
This is a method that was used in the old days. I love it! They stay fresh, and there is hardly any work involved during harvesting season
Leaving them in the ground
This is the best method, but if you live in a super cold climate, it is not ideal.
You'd not be able to get to them in wintertime because of the snow, and really had frosts will rot any part of the carrot that's above the ground.
Excellent in milder climates though!