William, you have to read the specs for the implement. If the manufacturer says it "requires" 30 hp, you can certainly use it on a 25 hp tractor, but may not have enough power to be satisfied with the results. For instance, a rotary cutter that calls for 30 hp may work just fine in grass behind a 25 hp tractor, but may not be good in high weeds or brush behind a tractor that small. I think you will more frequently find the horsepower rating for the implement to mention a range of horsepower; i.e., 25 to 40, in which case they are "recommending" a tractor with horsepower in that range. You will also find many that list a specific horsepower gear box. For instance, it may say a rotary cutter has a 40 hp gearbox. In that case, you can use it behind any smaller tractor that has enough power to do the job, and of course you can use it behind a larger tractor if you wish, and may be very happy with it, but if you tear up that 40 hp gearbox using it behind a tractor with more than 40 hp, the manufacturer may not warranty it. In other words, if they say it has a 40 hp gearbox or a 100 hp gearbox, they're staying that's the maximum power you can use and them still guarantee it won't break.
