All the weather above is delivered and updated in real-time. The main panel has the current weather (conditions right now), updated every hour, at the top of the hour. You'll also see the current wind speed and angle adjusted for the orientation of each park's batter's box. Below that, the game-time forecasts give you the projected temperature and rain for the three hours around first pitch.
For DFS or full season rotisserie leagues, wind and rain (rain outs) can play a huge role in your success. For example. if you were undecided on a #3 starting pitcher at Wrigley and the wind is howling in from left at 30 mph, that's your deciding factor. On the flip side, when the wind is blowing straight out, not a bad idea to stack a bunch of players in a daily contest... or, for roto, take a guy off the bench and hope he serves a couple balls into the wind. And, of course, the big red flag with weather is a postponement. We've all had players get an automatic goose egg just because we didn't move them to the bench in time... or it looked like the weather would clear. As a general rule, I like to bench guys whenever there's a block of heavy rain (>90% precipitation) for more than a few hours around first pitch.
There are a total of eight MLB stadiums that have a dome. Nearly all of the time, weather plays no role in the way and how far the ball travels. There are the rare times when a retractable roof is kept open even when it's windy, humid, or otherwise not perfect weather. Wind can sneak into a park during those brief times but, for the most part, always assume there's no fantasy impact in dome stadiums.
If you're in a season-long roto or daily league, weather issues here or there won't have a major impact on your numbers. If you're in a head-to-head league, where single games matter more, checking the weather should be part of your fantasy research... especially for your starting pitchers. Consistent wind of more than 15 mph in either direction can have a huge impact on your SP's performance. A long fly ball to left that gets knocked down by a strong wind could keep 3 runs off the board. That's huge for a smallish sample size.
On the flip side, if you're thinking about stacking a bunch of players on the same team for a daily fantasy team, definitely check on the wind. A single extra home run could mean >15 points (difference between in and out of the money in tight scoring).