Yes, the verb is simply "have." We use the same verb for "dream." You can have a dream, and you can have a nightmare.
We don't use "see" or "get." For "dream," it's possible to use the word "dream" itself as a verb: "Did you dream anything last night?" / "Did you have any dreams last night?" But "nightmare" is always a noun, and I've personally never heard it used with any verb other than "have."