It's skippable, but only after you've watched it once in full. Plus, you can't skip it with anything other than the A button - I normally mash the Start button so I can get the menu up to simulate to career player as soon as possible.I didn't have time to check it myself because of the other issues going on - it's meant to be skippable.
Considering the weather is for one whole day regardless of whether it's a 5 over match at 7pm, or a 5 day Test match, I've never paid much attention to it. It's easier just to look at the clouds in the sky or the actual rain.
Damn you Dutch!