The difference between settle, stay and wait...at least for my dogs is as follows.

Settle is a variation of the down command. For my dogs settle means to rest on their side instead of staying in the sphinx pose. It's harder for the dog to get up when they're on their side, which means that it gives me a chance to react if they're in stay.

Stay means stay here, do not move until I come back and release you. But you always always have to release the dog from the same spot that you were in when you put the dog in stay, otherwise you're teaching your dog that it's okay to break stay.

Wait is a command that means just chill for a second because another command will be coming shortly. I use wait most of the time in trials when I want a lead off at the start line or when the dog is on the pause table.

From my understanding a lot of breeds with short hair have problems with lying down on cold hard surfaces, really though you can't blame them it must get uncomfortable for them. All I can suggest is to get a dog bed or something to put on the hardwood floor for the dog to lay down on.