I don't suffer unduly from the cold, BUT like everyone else I do everything I can to keep warm(ish). This means I always go for layers of clothing starting with quality thermals, lined trousers building up to a wool jumper under my Paramo walking jacket and Muck boots. Head gear is my Tilley hat along with a large snood, the best item of clothing I have ever bought and perfect for keeping the gap twixt head and body warm. In really cold weather when, say, I need to break ice (not too often these days!) I do have chemical hand warmers as a standby....
I also have loose fitting quality ski gloves that can be easily and quickly removed for those occasions when I'm sitting behind rods for any length of time and when bites are more from luck than judgement ! Other, tighter gloves are used if float fishing.
On very cold days I will always wind in and walk up the bank for 10 minutes just to get the circulation going and inject life into my feet, BUT IMHO I see no other alternative to carrying plenty of hot WATER in my two flasks, with which I can make a variety of drinks, as the main means of instant heat and that feeling of wellbeing, if only for a short time....
I suppose the long and short of it is that I don't allow myself to get that cold that I'm not enjoying the session, and if that starts to happen I will come home. At 73+ I cannot afford to take unnecessary risks................
All in all I love winter fishing, with the cold just another challenge similar to that of being too hot in summer, and experiencing a lovely fish sliding over the net is worth all the discomfort. Nothing to beat it IMHO!!
To anyone trying it for the first time I can only say give every aspect of your comfort a lot of thought and perhaps try it during a relatively mild spell, first off. No real need to go out at the crack of dawn, as fishing either side of midday 'possibly' the best time to fish, BUT no set rule around this !! I would say 9am to 2/3pm ideal to begin with - that's my opinion anyway !!!
Good luck !
ps I don't know if anyone watched the prog on BBC4 last night about the climber Mallory and his team, attempting the first climbing of Everest which eventually cost him and others their lives. Wearing the best clothing of the day in -50 temps was never going to work......Our bit of chilly weather pales into insignificance, by comparison...