Carp can be caught all year even in December, historically I have had some good carp fishing in December when the conditions were good and only on commercials, some being better than others for winter carp however, I don't fish for them much now.
Roach available all year as well but in the really cold its usually only a few small ones I found. But January can be very good for roach, they come alive a bit after their lull in a very cold December; I think they have had plenty of time to acclimatize by then and get a bit hungry. But now through to December should be very good for roach although not knowing what the weather does these days can put all this out of kilter.
October sometimes good for last gasp Crucians and mild November days for last gasp Rudd I have found. But again who knows with the weather these days, was last December a record mild one?
However, the best winter fish by far are chub in my opinion, they will feed in all temperatures, I know some very good winter chub hot spots and they rarely let me down for one or two good fish.
I shall probably be braving the beach more this winter, bass to December, some big lurkers turn up sometimes, cod and whiting, dabs, hopefully the chip shop will be open on my way home ...