CE-680A flight crew reported landing safely after experiencing hydraulic system malfunction/failure in flight.

Narrative

HYD VOLUME LOW CAS message appeared when ferrying from ZZZ1 to ZZZ on Day 0 at night approx. XA:30z. Ran QRH; discovered it would take a while. Asked ZZZ approach to give us vectors to work the problem. He asked us what was the nature of the problem and I told him what it was; that we are requesting priority handling; roll the trucks; we will have to stop on the runway; runway XXL; and get towed off. We ran the QRH; got the landing gear blown down. ATC asked if we were ready to make the approach; and we thought we were; but as we were getting closer to turning base leg; we realized we needed to compute landing distance; so we asked for vectors again. We got everything accomplished and told ZZZ approach we were ready to make the approach. We had landing numbers for landing flaps 2; as well as for emergency braking. We landed safely and brought the airplane to a complete stop on XXL near [Gate] 1. The fire trucks came near while we waited for the FBO to bring a tug. We notified them about this while we were flying. The fire team stayed and waited for a while; but then finally left. FBO tug team showed up and got us chocked. I was then able to release the emergency brake. They towed us to the hangar. There was a puddle forming below the left engine while hydraulic fluid was dripping out of the drain mast. Hydraulic volume was showing 140 cu in. After getting towed and parked at the hangar at the FBO.Shortly after take off from ZZZ1; we smelled something not too strong; but strong enough to mention it. It smelled like deice fluid. It went away in about a minute. A few minutes later; while in cruise flight at 5000 feet; we got the HYD VOLUME LOW cas. We did not realize the two events were correlated until the next day when FO Person A mentioned it; and it suddenly made sense that was the smell.Suggestions: ATC is going to ask when are we going to be ready for the approach during any given situation involving delay vectors. It is up to us not to be pressured to be ready just because he asks. I was working the radios while FO Person A was working the checklist. I should have made sure we thoroughly checked over the rest of the QRH before we said we were ready to commence the approach. But the FO realized we had not done the landing computations yet; so we had to ask for delay vectors again. We got the vectors; and we got all the work done; and we finally approached and landed without any more problems.