I'd probably disagree... they should be thinned to about one inch or so apart. To leave them crowded is to invite disaster, since they simply won't grow properly. Although there are certain root worms that can cause havoc, I've never had a problem with slugs... seems they don't like the taste of the carrot tops. Make sure they get sufficient water... at least an inch per week, but not enough to leave them standing in water.
Here, in the western U.S., I leave them in the ground well beyond first frost. In fact, they can even be frozen in the ground, spaded up and used. I think the cold weather enhances the flavor.
Best of luck!