Yeah our shelter has stopped letting people adopt for the Christmas and new year period too. we're generally open to the public from monday to friday and the first saturday of every month, but around about the 10th December that all stops and we can focus a little more on anything else that needs to be done too. This year we still have 22 wild cats to neuter (they're caught in humane traps, vaccinated, neutered, de-wormed and then let loose again because they're too wild to home - and it's a no kill shelter), we have a new kitchen area going into one of the adoption rooms and we have too many cats in the home than we know what to do with. Some have gone home with temporary foster homes, some have had to scooch up a bit so that we can house them all. There's a really strict list of which cats get on with which, which cats need to be alone when they're out of the cages, which cats are on meds and can mix with others, which ones are on meds and can't mix..... it's a HUGE hassle for all involved, but there is no way we would let someone adopt over christmas, because when it has happened before, the cat has come back to us within a couple of months. People who adopt from us also get free vetinary care from the shelter for a year after adoption, so if the cat comes back to stay, we know fine well it's not because they can't afford the animal - it's just that they "don't want it". I hate that phrase.
So as Deb said, you'll probably find it very difficult to go to a shelter to adopt a cat.