It may surprise you, but westies usually rub their face and back to mark their territory. In other words to make their place smell like their home so it must smell like them.
You try to keep your home fresh, clean floor and carpets and here comes your westies and rub it all over with their smell as its their house.
Other reason why your dog will rub its face in the carpet is a desire to clean its face. There are two common times that your dog may rub its face in the carpet, specifically to clean itself. One is when your dog is done eating and it has small bits of food on its face and around its nose. In order to relieve the itchy sensation from those bits of food, your dog will rub its face in the carpet to clean off the food. Another common time is first thing in the morning. If your dog tends to wake up with eye rheum (or eye boogers), it is not uncommon for it to use the carpet to clean the rheum off of its face. While you cannot do anything to avoid the need to clean its face after eating, you can wipe your dog's face in the morning if there is noticeable rheum that occurs on a regular basis.
Although not as common as the need to clean itself, your dog may also be rubbing its face in the carpet to relieve itching and irritation caused by infections, allergies, and mites. The most common infection that would cause a dog to rub its face in the carpet is an ear infection. If you notice your dog rubbing its ears and face in the carpet on a frequent basis, look for discharge from its ear. If its ear is red and swollen, you should take your dog to the vet.
Sometimes your dog just enjoys rubbing its face in the carpet. There doesn't always need to be a reason why your dog is rubbing its face in the carpet. Sometimes dogs simply find that itching their faces in the carpet is a fun sensation, and they will do it just because it is fun. As with any pet behavior, if you keep a close eye on the frequency of face rubbing you will be able to determine quickly if it's being done for fun or because something is wrong.
Information taken from https://www.petbucket.com/blog/63083/4-reasons-why-your-dog-is-rubbing-its-face-on-the-carpet-.html
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