A300 pilot reported landing gear failed to retract after takeoff. The flight crew performed an air turn back and made a precautionary landing at departure airport.

Narrative

We were scheduled to Operate Aircraft X from ZZZZ to ZZZ on DATE. We showed at the gateway on time and it immediately started to heavily snow. The weather was calling for light snow and -3C. We blocked out on time after checking the airfield snow conditions and weather. We were informed of severe icing south of ZZZZ below 14;000 ft. Though we were north of those conditions we were also informed of less severe icing conditions in the local area. We pushed back and had directional control issues on the taxiways at ZZZZ. We coordinated for the clearing of the taxiways and returned back to the gateway. After closely monitoring weather; runway; taxiway conditions for approximately 3 hours with our Dispatcher and Assistant Chief Pilot we decided it was legal and safe to proceed to ZZZ. We then proceeded to deice (which took more than 1hr) and the departure runway while getting a last-minute update on the weather; winds; icing conditions and runway conditions. We also received a PIREP from an arriving aircraft. At this time the winds were picking up but we felt it was safe and concluded we were legal to depart. We departed from Runway XX and when we went to retract the gear it did not retract. We immediately tried the alternate system and then executed the checklist. The weather was solid all the way to FL250. Due to our weight and the gear stuck down we knew we could not get above that weather and our ceiling would have been around FL200. We were aware of the severe icing to the south of our location and did not want to get near those conditions with our gear down. We knew we would start to accumulate ice on our landing gear that was stuck down so we decided to [request priority handling] and to execute a quick return back to ZZZZ. We requested the priority handling; executed our ECAM and emergency checklist and then coordinated for short vectors to final to Runway XX at ZZZZ while conducting all checklist and runway landing conditions. We planned to do a CAT-2 ILS but ended up executing a CAT-1 procedure due to better ceilings; visibility and left crosswinds. The approach and landing were uneventful. We then spent approximately 1.5 hours coordinating with plows and ZZZZ Ground crews to park our aircraft at an alternate location.