Depends on lots of factors. Wind speed, wind gust, wind sheet, wind direction, turbulence, storms, snow, visibility, runway conditions, class of airport (ie which aircraft are operating there).
Certain carriers have their own rules too, for example departures can be prohibited if their is active storm/lighting activity within a certain distance of the airfield. Or for example, storms may be directly in the path of departures, but arrivals are ok, so only departures are delayed.
Wind limits and cross wind components vary between aircraft, approach and tower will allow aircraft to attempt the approach, which may end up missed or a landing. Pilots often ask approach if other aircraft are ‘getting in’ and if so, request to try the approach.
Here in Australia, most airport temporary closures occur due to storm activity - lightning (which also keeps ground staff off the apron), wind sheer, sudden wind change of direction as the storm is approaching (generally wind blows towards the storm as it approaches, and then as the storm hits, the wind swings to the direction the storm is travelling in). Only lasts about 15-20 minutes until the storm front passes, wind speed and direction settles, and operations continue as normal.
There’s not really an exact answer to your question.