We have researched this topic and it seems to depend upon state laws and even on previous case law whether a golfer or golf course can be held liable for an errant golf ball that leaves the property and strikes a vehicle, pedestrian, house, etc.
We have read that in many cases the golf course is not considered responsible for the actions of its golfers. Golf courses may have a policy where they will try to help find the golfer responsible but will bear no responsibility for errant golf shots that leave the course.
While state laws do differ in general it appears that many jurisdictions do not hold the golf courses responsible and in some cases the golfer is not held responsible either. This issue has been taken to court many times and the result in many jurisdictions is that there is not negligence on the golfer's fault since he or she does not know where the ball is going.
There is a theory of assumed liability in law which operates to protect such businesses as a golf course, an airport or other public access venues when you either partake of the services or know of the existence and continue to be in proximity. One lawyer we spoke to stated that you drove past the golf course with knowledge (under the legal definition) that a ball had the opportunity to travel outside the boundaries and strike your vehicle, therefore you have an unmitigated level of liability.
This information is from one lawyer in one state so your state laws could differ however in general even if there was negligence on the part of the golf course; you would have to prove that the owner's and employees exercised less than ordinary care in causing your damages in many cases to obtain a judgment against the golf course.
There are some lawyers that will take up a case against a golf course stating that it would be negligent of the course owner not to protect against such a foreseeable occurrence as a golf ball leaving the grounds. So you may find a lawyer that would take the case due to the fact no netting or fencing was placed around the area you drove by. If there were trees though that the course uses as a natural protective barrier your case may not be seen to have merit by a judge.
For example, a New York court decided on a case in 1991 (Rinaldo v. McGovern) by recognizing that merely because a golf ball does not travel in the intended direction does not establish a viable negligence claim.
In this court case an errant shot broke the windshield of a car traveling on a road adjacent to the golf course. The New York court applied traditional tort liability requirements that there must exist a recognizable risk and a basis for concluding that the harm following from the consummation of the risk was reasonably preventable. The court concluded that the game of golf is such that the risk of a miss /hit golf ball is not a fully preventable occurrence. In other words, the court said the risk was foreseeable, but not preventable.
Court cases we have read demonstrate that a golf course and golfer's duties depends on the particular facts of each case and state laws. If you did not inform the golf course of the golf ball striking your car at the time of the incident then it would not appear possible for them to try to track down the responsible golfer. So you may to now want to see if the golf course owners will voluntarily take responsibility for the damages. You may speak with the managers at the club house of the golf course to see if they have insurance that would cover the repair or replacement of your windshield.
If the course does not take responsibility then you can make a claim against your own comprehensive coverage to get your windshield repaired. In most states you will need to pay your deductible however in some states such as Florida, state law requires the deductible to be waived for windshields. Another option is to seek legal counsel to determine if in your state you can go against the golf course for the damages the golf ball did to your car.