This is not a rules question
The Rules of Golf govern how the game is played — where you can drop, what counts as equipment, when a stroke is penalized. They have nothing to say about what is in your bag to drink. Coolers are covered by course policy, which is set individually by every course, and that is why you will get four different answers from four golfers.
It also means there is no authority to appeal to. The pro shop's answer is the answer, and it can differ between the same course on a Tuesday morning and a Saturday competition.
Why courses restrict outside drinks
Two reasons, and they are worth understanding because they predict which policy you will run into.
Food and beverage revenue. The beverage cart and the halfway house are a meaningful part of what a course sells. A group that brings a full cooler buys nothing for four hours, and the course notices.
Alcohol licensing. A course that serves drinks holds a license to do so, and license conditions commonly restrict alcohol that the venue did not sell. This is why the policy on outside beer is usually far firmer than the policy on outside sandwiches, and why staff who will happily ignore a bottle of water will not ignore a case of beer.
What actually happens in practice
- Public and municipal courses. The most relaxed. A soft cooler bag, or a cooler sleeve that drops into a golf bag, with water and soft drinks is normal and rarely commented on. Bringing your own beer is against the stated policy at most of them, and how strictly that is enforced varies enormously.
- Private clubs.The strictest, and the ones where it matters socially. A member is responsible for their guest, and turning up with a cooler is the sort of thing that gets mentioned. If you are playing as somebody's guest, ask them, not the course.
- Resort courses. Usually enforced, because food and drink is a large part of the business model. Assume outside coolers are not welcome.
- Tournaments and charity outings. Often organized around a drinks cart or a sponsored bar, so outside coolers are normally excluded regardless of the everyday policy.
The size and shape of it matters more than the contents
A cooler sleeve that fits inside a golf bag reads as a water bottle. A hard cooler strapped to the back of a cart reads as a party, and it is the one that gets stopped in the car park. Golfers who bring their own drinks regularly use the small, soft, bag-shaped version for exactly this reason.
It also solves the practical problem. Golf is four to five hours in the sun; the beverage cart appears when it appears, and a bag-mounted cooler holds two or three cold cans without taking a hand or a cart-space.
What every course allows
Water. There is no course anywhere that objects to a golfer carrying their own water, and on a hot day the beverage cart is not a hydration plan — it appears roughly twice in four hours and it is not free. A bottle in the bag is normal to the point of being invisible.
The same goes for food you can eat quietly: a banana, a sandwich, an energy bar. What draws attention is a picnic, not a snack. If you are buying for somebody who plays in real heat, an insulated bottle and a bag-mounted sleeve between them solve the whole problem, and neither will ever get a second look in a car park.
How to ask, in one phone call
Ring the pro shop, not the restaurant, and ask two separate questions: can I bring my own drinks? and does that include beer? The answers are often different, and asking them separately gets you the real policy rather than the general one. If you are a guest at a private club, ask your host instead — they know what is normal there, and the question is really about their standing, not yours.
If you are buying a cooler as a gift
Buy the bag-mounted sleeve rather than a hard cooler. It is the version that gets used, because it is the version that goes unremarked, and it costs a fraction of the price. It also travels — it works at a cricket ground, a beach or a touchline, which a golf-branded hard cooler does not.
A cooler sleeve is a good example of the gift category that works best for golfers: things used around the round rather than to play it. That thinking is set out in gifts for the golfer who has everything.