It's a fleece polo neck all in one jersey.
I think lots of people who show dogs use them too.
The work by wicking the moisture away from the dogs body. If it's very cold I take one with me on my walk and when I get back to the car, I give brodie a quick towel down then pop his jersey on. It also helps keep the mess down till he dries out.
I also use it on old Hamish when we are out on walks to keep him cosy (he does not get wet), then swap them over in the car.
They are not cheap, but they last for ever and wash and tumble dry no problem. You can also use them after a bath if your dog likes drying itself on the carpet
I got mine on ebay. Just type in hotterdog. Or go to the main Hotterdog website just in case they have a sale on.
Others might be able to give you other sources or advice on similar jerseys.
I really do recommend them for keeping a dog cosy. And I use a very macho dog t shirt for old hamish too (it is black and says Security on it) It is made of cotton so he does not get hot, but it keeps his underbelly clean on walks. We get back to the car, I whip it off, and hey presto - a clean dog (apart from the legs

)