Most horsemen realize that weather can play a huge role in a horse's willingness, or lack thereof, to work. It seems so minor, yet can have a huge effect on a horse. On one hand, sometimes we have to work a horse regardless of the weather, but if we can be aware of the weather and its effect on our horses, sometimes we can even use the weather to suit us. So, let's briefly discuss how the weather can affect our horses, and thus how we can use it to our benefit.
No horse likes to be worked in the rain, and I think if our Quarab could talk, he would dryly attest to how rain that is pounding down all flashflood-style actually hurts your forehead (his nose intimately meets his chest in any rain that threatens his face). If you've got an experienced horse, by all means, ride away in the rain (though if you don't have to, for your horse's sake, maybe don't). For the horse-in-training though, I have to advise against it (usually), at least when the weather is particularly nasty and the rain is particularly coming down hard. It is one way to quickly make enemies (I mean c'mon, who actually likes working in cold, hard rain!?) and thus really does little positive for your relationship with said horse. If at all possible, save the really rainy day works for the experienced horse who is willing to oblige you thanks to your long-standing relationship. Don't forget too that riding in the rain has the added risk of a slip and fall. On the other hand, sometimes working in the rain just is not avoidable, and in areas where rainfall is a very common event (such as in lieu of snow), horses grow used to it and don't mind it so much.
Same follows for working in the heat - no one really seems to particularly enjoy the art of melting. On the other hand, got a high-energy, excitable horse? Ride her at the hotter times of the day. Riding a horse (lightly if possible, I might add) on a hotter day can increase your chances of a "good" ride and thus progress your training more easily. Horses tend to be calmer and lazier on hot days (just as with any living being) and thus are typically less inclined to raise a ruckus. Just be sure to not work too hard or long in the sun (if possible) and to provide plenty of water.
For the spooky or high energy horse, this can be another day to avoid riding (high winds, that is, not just some light breeze). Sometimes there is just no sense in playing with fire; doing groundwork instead can still allow for progress, at times moreso even than if you had ridden that day (and particularly if you were to have a poor ride). Think of it from the horse's perspective: the sound of the wind can mask a predator creeping up, and the waving grass could hide a lion as it creeps closer. Besides, who doesn't feel frisky in the wind? Obviously, for the experienced horse, wind is not a problem.
Those millions of white snowflakes converged on one spot can provide a fantastic exercise opportunity for your horse - wading through drifts and working through snow is a wonderful way to work off a few excess pounds. Just be cautious of grip (or lack thereof) beneath the snow and keep in mind that your horse may feel pretty good on a cool crisp day as well ;)
For the horse who typically lacks motivation, avoid working her at the hottest part of the day and instead work her in the morning or wait until evening. They will be a lot less grumpy with having to work and will be more inclined to follow your direction willingly.