Air carrier Captain reported engine failure while taxiing to the gate.

Narrative

During winter operations we arrived at the aircraft noticing there was snow and ice behind the engine rotors all the way through the back of the engine. There was a lot of confusion from operations when we told them that we needed the engines cleared of snow. They just kept telling us to go to the deicing pad for de icing. So we called the de icing frequency and they told us to call maintenance. Which we did; as well as an ELB (Electronic Log Book) entry. Maintenance finally came out with guys from the de ice pad. When they finished and cleared the release; I had the relief pilot inspect the engines. We never got a straight answer but it looked like they did not use hot air inside the engine but possibly fluid. We proceeded to the de ice pad and after a failed first de icing we tried a second attempt but within 3-5 minutes on each attempt the anti ice fluid failed because it was snowing so hard. During the taxi period we performed several clear engine run ups per the FM (Flight Manual). At this point we taxied back to the gate; while we were waiting for the parking crew the right engine oil pressure gradually dropped over a 5 second period to 7 psi and then the engine failed. At this point we shut down both engines and were towed to the gate.I do not know if the engine failure was related to the engine de icing technique or not but maintenance was fully debriefed at the gate after engine failure as well as an ELB entry.