With Bethesda calling this a 'pre-beta', it suggests there might be a full 'beta' down the line, so if you miss it, perhaps there's another chance to play. You can play the Fallout 76 free trial between June 10 and June 17, which is the same time as the Nuclear Winter beta. Fallout 76 Nuclear Winter beta dates, and error code 4 8 2006 explained

The mode continues to give the bizarre, boring and broken game another shot at redemption after a series of updates since launch, with the limited time mode coming with a week-long free trial. The Fallout 76 Battle Royale mode Nuclear Winter mode was one of Bethesda's surprise E3 2019 announcements - introducing a major new mdoe to the game.