Are dogs affected by dwarfism?
The short answer is yes, other animals can experience dwarfism, including dogs, although it may not be what you are expecting.  Dogs are apparently particularly susceptible but they often are a special case.  We've so heavily bred dogs for whatever traits we desire, so now entire breeds are affected by dwarfism, such as dachshunds and corgis.

The reality is that dwarfism is a mosaic, with many types, and shouldn't be classified under one umbrella.  You're probably mainly thinking of Achondroplasia, which is just one of many causes.  You may also be aware of Hypothyroidism.  Not every case looks like others, so in animals it may not be what you except.  Other animals are susceptible, such as the sheep mentioned in the above articles, and horses, which are also a long-time target of selected breeding.