How to filter through an array object based on property inside of it?

What you can do is

1 - Filter the data first and map the filtered data in your render.

const weather = this.props.weather.weatherData;
const weatherFiltered = weather.filter( ({ isDayTime }) => isDayTime );

return weather.map(weather => {
    return (
      <div className="ui segment">
        <div className="ui center grey aligned header">TheDay</div>
        <div className="ui center grey aligned header">
          <i className="sun icon" />
        </div>
        <div className="ui center grey aligned sub header">
          Min:75° Max:80°
        </div>
      </div>
    );
});

2 - Map in your render and return null when you don t want an item to be rendered.

return weather.map(weather => {
  if (weather.isDayTime === true) {
    return (
      <div className="ui segment">
        <div className="ui center grey aligned header">TheDay</div>
        <div className="ui center grey aligned header">
          <i className="sun icon" />
        </div>
        <div className="ui center grey aligned sub header">
          Min:75° Max:80°
        </div>
      </div>
    );
    return null
  }
});

use filter on weatherData and return items that match the condition.

const weatherData = this.props.weather && this.props.weather.weatherData || [];
const weather = weatherData.filter(weather => weather.isDayTime === true);

return weather.map(weatherItem => {

    return (
      <div className="ui segment">
        <div className="ui center grey aligned header">TheDay</div>
        <div className="ui center grey aligned header">
          <i className="sun icon" />
        </div>
        <div className="ui center grey aligned sub header">
          Min:75° Max:80°
        </div>
      </div>
      );
    }
  });
}