I've included webster's definition of a veteran and it doesn't mention anything about war or combat. The Veterans Administration says the following about who qualifies for veterans benefits:
Basic Eligibility:
A person who served in the active military, naval, or air service and who was discharged or released under conditions other than dishonorable may qualify for VA health care benefits. Reservists and National Guard members may also qualify for VA health care benefits if they were called to active duty (other than for training only) by a Federal order and completed the full period for which they were called or ordered to active duty.
Minimum Duty Requirements: Veterans who enlisted after Sept. 7, 1980, or who entered active duty after Oct. 16, 1981, must have served 24 continuous months or the full period for they were called to active duty in order to be eligible. This minimum duty requirement may not apply to veterans discharged for hardship, early out or a disability incurred or aggravated in the line of duty.
So to answer your question, no you don't have to be in a war to be a veteran you just have to serve in the military. Now if someone says they are a "combat" veteran, than most likely they did serve in a war but you're better off asking them, I'm sure they'll be glad to share their story with you.