As long as you have a pit with a solid bottom that will catch all the ash and coals, you should be fine. I've been told in the past by CO's that the ash left behind from fires right on the ice will sink down and can coat the bottom and contaminate spawning beds. Not to mention all those lovely black coals floating around in the spring, washing up on beaches.
Mmm, roasted lunch over a fire, reminds me of when I was a wee-one!