Air carrier Captain reported finding ice accumulations on the aircraft after a gate return due to deteriorating weather conditions and after deicing was complete.

Narrative

After arriving at the airplane and reviewing weather conditions myself and the First Officer (FO) contacted the deicing coordinator to have type 1 and type 4 for the whole aircraft applied. The conditions at the time were -SN and -8C. Deicing took almost an hour and we finally got a call from the ramp crew stating they were ready to push. Not only was there still a significant amount of ice on the nose and windows; we also never received fluid type or other Deicing information; so we called the deice vehicles back. Once we had finally received the proper treatment; we coordinated with Dispatch to offer egress; since we had been delayed significantly. Once we finally commenced taxi; the ATIS had updated to -FZDZSN and outside conditions had deteriorated significantly. We updated our deicing app and noticed we needed to do a nose check. We saw ice on the nose and windows and decided the nose check was not satisfactory and hence decided to do a wing check after we got closer to the runway. Due to outside conditions and pax windows being frozen and not being able to see; we decided to do a gate return. Once we arrived at the gate; the FO and I did a walk around and noticed a lot of ice. Flaps were set just prior to runway; then left set after return to prevent damage and operations was notified.