If it’s the dog’s nose, the first is the thing to aim for…if it’s the dog’s owner, try for the second.
And don’t stop at the temperature or dryness. Add something soft to sit on, a cup of tea, and a good book to read. The dog may not care for the literature, but if there is a plate of biscuits with that cup of tea, he will be prepared to take an interest.
Now the cat has a different attitude. Oh, he doesn’t like cold and wet outside any more than the dog does, but if it is a case of being annoying and making the human owners get up and down repeatedly, he is prepared to go in and out of the door all night. This is interspersed with time spent in the warm and dry, but generally in the middle of the bed.
We don’t keep fish, so their attitude to warm and dry is unknown. Ditto a bird, though I think they would be pretty much in agreement with the dog. I suspect they would wait until the cat was out and then hide the door key.