Equipment like this will get water in the oil without having any place for water to "leak" into the system. The oil is somewhat hygroscopic (attracts water, similar to brake fluid) and relies on heat buildup from hard use to keep the moisture driven out. Once the oil becomes milky looking, you can let it sit for months and the water will not fully separate. Some will separate, but unless the container is tightly sealed, the oil will continue to pick up additional atmospheric moisture primarily due to temperature changes. The one gallon at a time routine in a crock pot would work, and there's no harm done to the oil by heating it, but it would be a real PITA doing it a gallon at a time if the system has much capacity. You can buy immersion type thermostatically controlled heaters on Ebay on a regular basis, often brand new, for less than $50. If you weld a pipe coupling into a 30 or 55 gallon drum, screw in one of these heaters, and wrap the drum with insulation, you'll have a perfect hydraulic oil "dryer". A drum with a removable top works best because it lets the moisture disperse into the air more easily. A closed top drum will tend to let the moisture condense on the inside of the drum top and drip back into the oil.
Regarding the question of whether or not the moisture is harmful, most manufacturers of hydraulic equipment will tell you that, aside from materials or workmanship failures, roughly 90% of all hydraulic component failures are due to moisture in the oil.
My dad was in the crane business for 34 years. During the time when most concrete was poured with a crane and bucket he had almost zero hydraulic problems with the cranes because pouring concrete works a crane hard and keeps the oil hot. Most all the cranes would pour concrete for a full day at least once every couple weeks, and the oil was always clear as a bell. As concrete placement moved more toward pumping, there was little opportunity to do any type work that would load the machine in a similar manner. Problems became much more frequent, and were water related almost every time. We started changing and drying the oil via the method outlined above on a regular basis years ago, and it took care of most of those problems. Some of the oil was probably close to 20 years old, but any time we ever sent samples off for analysis, we never got a report back indicating the oil was "worn out". We kept a couple hundred gallons (enough to change the oil in our largest machine) dried and in drums. When changing the oil, we would pump the old stuff out and put in the dried oil, so we could then dry out the removed oil without keeping a machine down. Over the years we probably saved over $50,000 in oil that would have otherwise been thrown away due to moisture contamination.