I rely on two indicators for weather: my sinuses and Forecast.io.
When I'm already congested, a strong weather front will give me a blinding headache. (Like today.) But that's not helpful for you, or Daisy, our bichon frise, who hates having a potty walk in the rain.
I recommend Forecast.io for amazingly accurate hyper-local, minute-by-minute weather forecasts, which sometimes (alas, not quite, today) gives the dog enough time outside to do what she must.