Peter wants to have a snake as a pet.
In general, the term 'raise' refers to caring for an animal from birth in a farm or zoo setting.
You will occasionally hear, 'He keeps a ______ as a pet,' but this construction is most frequently used when discussing an unusual or exotic animal. 'He keeps a skunk as a pet.'
When referring to dogs or cats, people 'have' those as pets.
Student or Learner