Hi Gill,
I would say if the water is still liquid, then you can still catch Carp, however IMO you need to look at a water that can reward your efforts! And I mean this in the nicest possible way, for me to endure freezing conditions, I would need to be in with a chance of a descent fish as it is hard work in -10c with long periods of darkness!
A good bedchair is a must, also a good ground sheet will keep down the damp from the ground, and also cooking gear for hot drinks and food, as for clothing you need layers that will trap your body warmth and water proof/ wind proof over wear to keep you dry and protected from the wind, good thermal boots and socks, if your feet get cold you will be cold allover! Spare socks, and keep them dry, you can warm them in your sleeping bag! As damp =COLD! A big old wooly hat is a must as so much heat is lost through the head.
Warm head and warm feet, you will enjoy yourself, and if you are warm and happy, then you will fish well!
Lastly the very inportant thing is to let people know where you are, and have a mobile phone with you! Winter Carp angling can be great if you get it right, but can be very dangerous if things go wrong! So plan and prepare well for your sesh and enjoy!