Q: Now that water temperatures are dropping, what area of the lake am I most likely to continue catching big carp?

A: Shallow areas and the margins are certainly worth trying throughout both the autumn and the winter, even when there has been a frost.
The reason is that on bright, sunny days shallow water warms much faster than deeper water, even in winter.
To increase your chance of catching, fish after a mild spell.
You will also find that carp shoal up very tightly when it's cold and they feed for very short periods, so if you do gain a take expect another from the same area quite quickly afterwards, particularly if you are fishing a heavily stocked water.

John Wilson:Angling Times October 24 2006.

Size matters "when water temperatures drop, it's time to re-think your terminal tackle"

Q: Should the size of the hook change from summer to winter fishing?

A:Fishing for all species gets much harder during the winter, so step down your hook size to get bites. Use thinner lines, too, and more delicate presentations.
If you are a carp fan and fish with hair rigged boilies and baits you should still drop down a hook size or two. This also applies to specialist barbel fishing on rivers.
If you prefer fishing with maggots throughout the year you might be using a size 18, or maybe a size 16 for double maggot during the warmer months, but in late autumn you should aim to start with a single maggot presented upon a size 20 hook, or even a size 22 if the going is really tough.
Hooklength lines ought to be reduced too. Try floatfishing with 0.08mm or 0.10mm hooklengths, or even 0.06 or 0.07 if you have a light actioned rod.

John Wilson:Angling Times October 10 2006.