Hi
I do it all the time, the head and neck. That does not effect whether they stay warm or not. In fact on the warmer days during the cold days, they really like that hair off and get too hot.
It is the hair across the top of their back/withers that keeps them warm. If I were showing in Jan I would do full body clip now. So I can see how the horse is shaping up. I would double blanket on days they need it, with neck wrap and slinkie, heat lamps if necessary. They are toasty warm that way, believe me. It only takes a short period of time for their hair to grow enough after winter clip to help keep them warm even though it still looks really short.
I like to see a pretty head any time of the year. I have seen some clips that do the head and part of the neck too, just under the throat and angle on the neck.
Good luck at your show!
Beth