This is so low-pressure, it's great for a first date (or fifth, or a fiftieth). When you're on a date, you don't want the stakes so high that either party looks bad if they don't have the training necessary to complete the task (think tennis or skiing), but not so low that there's no room for a little flirtatious competition.
Since a mini golf course is usually built for kids, it's going to be simple enough to complete, but gives you something more to do than exchange questions over drinks. If it's the first date, leave it at mini golf, since you don't want a first meeting to last longer than a couple of hours anyway. If it's further in, go to dinner or drinks after the golf, and make sure to set a fun, flirtatious bet before you begin!