EMB-XRJ pilot reported during the landing roll experiencing a hydraulic system failure resulting in loss of steering control and the aircraft needing to be towed to the gate.

Narrative

Background Information:Weather at ZZZ:Visibility - ¾ SM Light Snow / Blowing SnowILS XX in useNotams:RWY XX RCC (Runway Condition Code) - 5/5/5Ramp and Taxiways - Braking Action PoorNumerous Taxiways Closed on Field including Runway XY/XZ closedPerformance numbers for landing:Landing Weight: 38;300 LBSLanding Distance Required: 4918'Flaps 45Vfs - 154Vref - 123Vga9 - 141Vap - 137Approach Briefing. ILS XX was chosen as the approachThreats Briefed Runway Conditions - 5/5/5 - Landing DistanceMitigation - TR (Thrust Reversers) used for landing and flaps 45 for slower speedNo float land in the touchdown zoneApply brakingPossible snow on runway Mitigation - Firm Landing to get the wheels on ground and penetrate the contamination Taxi Way Closures - High Speeds were closed - had to taxi to the end of Runway XXBlowing Snow - Talked about the visibility restrictions and depth perception issues that arise from having snow blow over the runwayApproach was uneventful. Snow was not a factor in terms of visibility as we could see the runway and lights from the FAF.Maybe some glide slope adjustment at the end due to wind changes. We were within stable parameters. Approached one dot high at some point beyond the 1000' callout. But was corrected by 500'Came over the threshold about 70' AGL Landed about 500' beyond the 1000' markers - approximate - could be closer to them than 500'When landing we adjusted for the cross winds. The crosswind was from the right.Flare and touchdown felt normal and not as hard as I wanted.After all 3 landing gear had ground contact I applied the brakes. The braking action was good for the entirety of the runwayI started to put the thrust levers into thrust reverser mode.I requested Full Reverse thrust.As I was bringing the thrust levers over the fence" we got a caution message. ENG1 REV DISAGREE - I believe I saw this for a very short time.We yawed to the right a little bit and pulled us off centerline. Maybe 5-10'; not much. I corrected with left rudder. The rudder input stabilized the yaw. As we slowed I needed less and less rudder to correct and at the 80 KTS call out I stowed the Thrust Reversers and went to idle thrust. I started at this time to correct us back to the center line and noticed more EICAS messages popping up. Spoilers Fail was next and as we slowed I noticed HYD SYS 1 Fail. About this time I started to notice that the brakes did not feel equal; the left brake to me was further forward than the right brake for the same foot pressure. As we slowed I realized we lost Hydraulic System 1. I said to Person B that we will not be able to steer the plane and as we were very slow like 2-3 kts I attempted to use the tiller and then the rudder pedals to steer. There was no response. Tower said that we "could Take [Taxiway] 1 if we wanted just caution it was not plowed as well as 2" I came to a stop on the runway at the 2000' sign marker before the intersection with 1.Person B informed the Tower we were stopping on the runway as we had an issue and had to work a checklist (This is paraphrased as I don't remember the exact wording)I brought up the hydraulic page and noticed no pressure and that the electric pump was not running.I turned the electric pump on for a moment to see if that changed the pressure it did not so I turned it back off. I then called for the Hyd Sys 1 Fail QRHThe EICAS Messages on the screen at this point were:Cautions :Spoiler FailRudder Sys 1 INOPHYD Sys 1 FailAIL Sys 1 INOPAdvisories:HYD1 Lo QTYWe went through the checklist. The checklist told us to shut off the electric pump.We also noticed while running the QRH that there was no hydraulic fluid any longer for system 1. When I checked it in flight it was near full. The last time I looked at the hydraulic level was in the descent. As we discussed the inop equipment due to a loss of HYD SYS 1 I told Person B about how the brakes did not feel even or normal. Tower queried us on status and I stated we are disabled on the runway because we lost a hydraulic system that controlled our steering.The Tower gave us priority handling and asked for fuel and souls on board. We asked the Tower to bring a tow to get us back to the gate. Tower stated they were bringing fire rescue out to us on the runway along with a tow. The airport at this point was effectively closed.I briefed Person C (Flight Attendant) on our situation and briefed the passengers. Letting them know that fire rescue was coming as a precaution. I then updated Dispatch on the situation and gave some background on what happened.As we had some time I discussed the incident with Person B. Talked about how I thought we had a leak in the hydraulic system 1 and I tried to think about when it happened. I stated it had to be after we put the gear down because we did not have any EICAS messages then. I concluded it happened either while on short final or touch down.As we were waiting I decided to keep the engines running. My thought was that if we needed to get off the runway in an emergency that I could use differential braking and thrust to do so.At some point we completed the after landing check (modified) we left the TCAS in TA/RA mode for us to ensure no issues / conflicts in case someone was going to land on the runway. We also left all of the lights on for visibility of us on the runway. Fire Rescue came on scene and we discussed if anyone was hurt or needed medical attention. I stated no. I did say I believe we had a hydraulic leak and I was worried about a possible brake fire. They stated they were going to check out the aircraft for leaks and also stated they had a FLIR camera on our brakes to make sure there were no fires.After the inspection nothing was found on the aircraft out of the ordinary. We let them know that it would be prudent to do a FOD sweep after our landing to find if we left any Hydraulic oil on the runway.It took a while for the tug to come out - mostly because of how much snow was on the taxiways.The tug was about to connect up to us and we shut both engines down. We completed a modifed parking check to ensure we were ready to tow. We left the TCAS in TA/RA; Hydraulic pump 2 on; cabin signs stayed on as well as strobes and beacon.Once we were under tow and off the runway we switched to ATC-ALT mode for TCAS. And the lights were shut down less nav lights.We were towed to [Gate] XX. No one requested medical attention and everyone deplaned normally. Fire rescue came on board to tell us they found a puddle of hydraulic fluid on the runway a short distance behind where we came to a stop.Contract Maintenance noticed the hydraulic oil on the left inboard spoiler. He surmised the actuator for the spoiler failed upon landing and leaked all the fluid out. The spoiler was slightly up maybe 1/8' up from the other wing panels when we were at the gate.I found out the next day the spoiler actuator and the engine driven hydraulic pump were replaced. The hydraulic pump was replaced due to it running dry for an extended period of time.At the hotel once I had some time to breathe; I went through a debrief with Person B we discussed the course of action and agreed our actions were appropriate for the incident.Things I would do different.I maybe would at least shut down engine one a little sooner. - I am 50/50 on keeping the engines running but seemed like the right call at the time."