Great question there, Oh Nameless One. I would suggest bringing a micro-fridge with you in which to stock your beverages. You might want to think about a full-size fridge if you know you're a heavy drinker.
Of course, you're going to need power on those particularly hot days when simply carrying an unplugged refrigerator just won't cut it. Likely, your best bet (given that most disc golf courses do not have amply supplies of power around) will be to bring a generator. I'd suggest one without wheels so you don't leave unsightly tracks on the course.
Finally, expect to pack some extra extension cords in your disc golf bag (which might mean removing one or all of your discs). Three miles of cord should suffice, or more if you are an inherently bad player and will be doing some wandering.
Note: bringing around a backup generator is HIGHLY recommended if you require your drinks to be chilled at all times.