It depends on how you're planning on packaging the chicken, and what you're eventually planning on doing with it. Regardless I'd remove it from the bone and either cube it or shred it, package it in predictable serving sizes (enough for 1 meal or 1 casserole or whatever you might use it for) and freeze it that way. Alternately you can take the prepared meat (cubed or shredded or whathaveyou) lay it in a single layer on a baking sheet lined with parchment, freeze until solid and then put all of it into a large ziploc so you can pull out just what you need.
As for nutrients, i don't know that you're going to lose any more nutrients from freezing than you lost through cooking. You risk compromise of texture, the possibility of freezer-burn and maybe drying out the meat, but it's not a "risky" proposition. Cooked meat, unless it's vacuum sealed might last 6 months in the deep freeze. Beyond that, again it's not "bad", but you risk a compromise in flavor.
