Thanks for the reminder, I'd better get my purple carrots into the freezer before they go fuzzy, since they're not top of the to-brew list at the moment...
For a gallon of carrot wine, Terry Garey recommends simmering 5 lb finely sliced carrots 30-45 min until tender, and using the water. Add 10 bruised peppercorns if desired, then strain it all out and use the juice (then the carrots can be eaten separately, although I suppose if you ferment on the carrots you could use it for drunken carrot cake later). 3 lb honey, 1 tsp yeast nutrient, I'd also add 1/4 to 1/2 tsp yeast energizer if you have any. She also suggests using juice and zest of 3 oranges and 2 lemons so you'd need pectic enzyme if you followed that (this is a wine recipe originally, so we want to skip the acidity if making mead), but you could probably skip the pectic if you just used zest.
But using roasted carrots could be a really cool twist on this recipe, get a little of that caramelized bochet thing.
I think when I use my purple carrots in a mead, it'll be with 3 lb honey and I will grate the purple ones and ferment 'em raw (perhaps scalded to set the colour) and maybe I will roast any non-purple ones (I get 2 lb bags of mixed "heirloom" carrots with purple, white, orange, yellow and sometimes pink carrots), and use zest of a couple oranges.