Where winters are milder I wouldn't think the mulching and timing would be as critical as for a harsh climate. I wish I had more knowledge about this for other climates. Yes it is important to have them at a good size by the time the colder weather starts.
Soil is very important too. I never dig my ground. I only add mulch and compost to it in layers and my ground now is very soft. I never have to thin my carrots. The carrots I just pulled from my garden were all in a group touching each other and none were crooked or curled around each other. As they grew the loose soil allowed them to push away from each other. Any weeding that it needs is actually fun. It pulls out so easily but you only need to run the rake through them and they pull up and eventually becomes nurishment for the soil.
My soil is built up each fall with compost made from seaweed, kitchen scraps, weeds (without seedheads), wood ashes, chopped up dry leaves and any old soil. I never mix it so it takes about 6 months to a year before it's ready to put on the garden.
When I first started my garden my carrots were very disappointing. They were crooked, hard to pull out of my compacted soil, critters got at them and they were not sweet. My improved soil has changed all that. It has taken 3 years to get it to where it is today but I saw an improvement the first year I applied woodchips as mulch. Now I'm using chopped leaves because I'm running out of woodchips.
Here is a picture of the carrot bed taken this past summer that we are now eating from in January.
This year I will plant several more beds of carrots now that I know I can overwinter them.