Most industrial or fixed plant hydraulic systems tend to use "hydraulic oils" such as HLP or HV types etc. The problem with using an SAE 10W is the demulsibility characteristics (water separating qualities). Industrial hydraulic oils are designed to separate from water easily. Engine oils on the other had contains detergents which has a tendency to hold or emulsiy the water.
The other issue is air release qualities (always done on all industrial oils - check technical data sheets of oil supplier)- an ISO VG68 oil for instance will have an air release of 6 to 8 mins. It's important so that the hydraulic operation is not spongy and you want rapid response. This is not a typical test or characteristic of engine oils.
Multigrade engine oils (eg 10w/30)also contain a viscosity index improver polymer which are sheared down (ie chopped up)when used in hydraulic systems both mobile and fixed plant application - shown as the reduction in viscosity. The rate of shearing is dependent on the type of pump ie piston or vane or gear.
Filterability is also important - industrial hydraulic oils are checked for filterability - as there are many fixed plant applications with fine filters. This is not a test done for engine oils in general.
A few OEMs recommend an ATF style fluid - most ATF fluids are equivalent to an ISO VG 32 or so hyraulic oil. Not exactly sure why but it can be down to their experience with ATF fluids only and not much experience with hydraulic oils. Many ATF fluids are made on a high quality base oil (eg group III or higher)which imparts oxidation stability to the oil.
However, most hydraulic oils are made on quality base oils with very good antioxidants.
I hope this helps.