Air carrier pilot reported during push back the tug slid temporarily out of control on an icy ramp. Later on at the deicer pad a deicing truck collided with the aircraft.

Narrative

Prior to this event; operations were normal and rest was managed well on this trip pairing. Today we experienced problem after problem that constantly developed threats that we had to tirelessly mitigate; which caused a great amount of mental exhaustion along with physical. I started the day at XA00 local time to be report for our XB04 local time transport to the airport. While completing my preflight duties; I observed zero items with the aircraft logbook that were of concern or could cause a delay. Upon reaching [the] departure gate; the Gate Agent stated something completely out of the ordinary; which put the Captain and I on alert. The Gate Agent stated you should do a thorough walk-around because the previous crew from the night before reported a hard landing." I was confused as to why we were hearing this from a Customer Service Representative. Regardless; there was nothing in the logbook; but given the report we had to investigate by contacting Maintenance that then required a maintenance inspection. This station utilizes contract maintenance that is only available after XC00 local time. Due to the snow storm that ZZZZ was experiencing that reported it would take about 30 minutes for contract maintenance to reach our aircraft. Just this started our delay. Upon reaching the aircraft visually; I observed that the flaps were left extended overnight; all tires appeared to have low tire pressure; one of our hydraulics quantities was at Refill (RF); both engines had multiple inches of snow and ice blocking the intakes; as well as both N1 fans being frozen completely and unable to move. While experiencing coordinating more maintenance this required multiple trips to and from the flight deck to the outside of the aircraft in sub-zero temperatures; falling snow; and a snow covered icy ramp. After waiting over 1.5 hours; maintenance was complete; then it took an additional 30 minutes roughly to obtain our Maintenance Release. After this; we were ready to push; but the ground had left and there was not a tug connected to the aircraft that caused even further delay. After some time; we acquired a push that was only able to push about 3/4 of the way due to the tug slipping with the aircraft connected. We set the parking brake as instructed and completed the push in the position we stopped in. Both engines were then started and given the snow storm conditions; the de ice pad became full which caused us to wait even longer. All of the constant changes and trapping of potential threats was becoming mentally fatiguing. Finally; we were cleared to the de ice pad and expected to then make a normal departure. Towards the end of the final application of anti-ice fluid; ground personnel called us to notify that one of their trucks slowly collided with the aircraft. Due to this; we had to return to the gate for another maintenance inspection. Now we hit the Long Tarmac Delay point; required more fuel; and the Ground Crew took a while to direct us into the gate. At this point; multiple hours had elapsed with high workload. We prepared the aircraft again; pushed back and the tug had to stop again due to braking action. After starting both engines; with the parking brake set; we began to slide on the apron. Due to this; we shut down in position and waited about 20 minutes for snow removal equipment to clear a safe path for us to then taxi to de-ice that added even more time to the multi hour delay. Following this we made a slow taxi across the airport and made a normal departure and operated the flight to ZZZ. By the end of all of this it was my best judgment to call fatigued due to the multiple hours at a high workload."