What has the more epic feel to you? Ten heroes stand in the middle of the path, the sun high over head burning bright in the clear sky as the armies of Sharak Doom descend upon them. They must hold the path for at least an hour to let the near by town evacuate.
Ten heroes stand in the middle of the path, the sky crackles with lightning as freezing rain pours down upon them. Descending upon them, boot stomps sounding like rolling thunder, come the forces of Sharak Doom. They must hold the path for at least an hour to let the near by town evacuate.
Granted, both are fairly epic, but (to me) they have a different feel. In the one with the sun burning high, we have a bright and clear day, it feels more heroic. The light illuminates everything as the forces of good stand against the forces of evil. On the other hand, the freezing rain and lightning gives a darker feel to the other one. It feels more desperate as the heroes brave the elements and plan to make their stand against the forces of Sharak Doom (you can use that btw, free of charge).
Hopefully looking at that you can get an idea of how useful the weather can be in the feel of things, but also think about the other options it gives you. Heavy rain makes for bad footing, people can slip and fall, you can throw out those in descriptions, have people trying to scramble back to their feet. Make the fight feel a lot more alive and kinetic just because the weather allows you to put those things there.
These benefits don't stop with just the weather, day and night can also work, as well as any number of other things. Describe the area, don't go into crazy detail but give the key words, freezing rain, cold air, strong winds, desert heat, like an oven. These are all quick phrases that don't just convey what is going on but an entire environmental feel. Most people know what it is like to be out in the freezing rain for a few minutes, their mind can extrapolate on that for a few hours fighting. Go into other things too such as the sharp rocks, steep mountains, make the land scape welcoming, foreboding, dangerous, whatever you want. You can even flat out say that "the mountain has a foreboding slope to it" and your players will get the idea. It is heavy handed but it works.
The point is that the environment around a place can do more to set the mood for you than any number of pages and words of description. Think of the cliche places we have, like the Mad Scientists' lab we get with the dark sky and the lightning crack above. This conveys a message faster than any description could, and we can use it. Look to the Two Towers movie and the battle for Helms Deep. Not only is it night, and the people of Rohan are surrounded by a force 10-100 times their size, but it starts raining before the battle. The rain conveys more of a sense of the depression and gloom the scene should have than the ten thousand CGI orcs. This is even more impressive when you realize that rain almost always favors the defending side in a siege. So this thing that is helpful to the heroes makes us feel their plight even more because not only are they standing against 10,000 orcs waiting to rip their throats out, but they're doing it while standing in the rain.
Another example? Think of a scene, the hero gets to the bombed out building and finds the body of the girl. He picks her up in his arms, and drops to his knees to scream out her name. 10-1 odds that it is raining in the scene. We'll probably even get a close up shot of their face, just to show that they are crying and that isn't just rain pouring over them. Use rain for sad scenes, the sun breaking through the clouds can show the birth of hope or a sign that all isn't lost. A windy night whipping up dust and what ever it can find can show the chaos and confusion of a situation.
Now, what if you don't want to just use the environment to convey emotion? Well you're still in luck. Bad weather can be used as plot points in a lot of ways too, especially in fantasy worlds where there is often a sense that the King is bound to his land, and what befalls one befalls the other. Bad weather can also be used to make the environment itself an opponent. Yes, you want to go outside and look for clues, but there is a blizzard out there so it is dangerous. Go out too long and you could be hurt. Odd swings of weather can foretell of mystical plights coming in the distance. The possibilities really are nearly endless when it comes to this. Just needs a bit of brain juice and the willingness to use it.
As an example, my plan is to make the weather a key feature of the next Greymoore game I run. In the system update I will cite the weather at certain places and show what I was trying to go for. It is going to be a bit of an experiment for me to do, so hopefully it will work out.