1. Don't compete in outdoor archery.
2. Learn to shoot despite wind and rain.
Now I am not suggesting you just give up and do number 1. If you give up that easily due to a little wind and rain you seem to be missing the point of outdoor archery - and likewise outdoor archery competitions. The wind and rain (and heat) is supposed to be an added obstacle.
I once did archery on a very foggy day and I have to admit it made it a lot more interesting having a blurry target in the distance. And it really didn't effect the quality of my shots once I got over the unfamiliar environment.
Taking positive and preventative action will help you get better results. Fussing over the weather conditions won't help you, but being proactive about them will. Take your time like you would during a normal shot. Don't rush it just because you want to get it over with.
Some people have more difficulties than others shooting in the rain. They think things like "I suck at shooting in the rain. I always shoot badly in the rain." Etc. However that negativity is a mental block. You can adjust for rain conditions very easily.
For example if you practice shooting in the rain regularly you may realize you shoot several inches lower in heavy rain. You can correct this by simply adjusting your shot upwards by the same measurement.
Depending on how heavy the downpour it is you may have to adjust your shots a different amount. If it is barely spitting outside then you don't really need to adjust your shots at all. "It is the arrow hitting the rain, not the rain hitting the arrow."
Dress appropriately. Always bring your rain gear to competitions because you never know when you might need it. Waterproof boots or shoes, a towel to dry off your equipment, a large umbrella, wide brimmed waterproof hat (Stetson cowboy hats work great), a tight-fitting jacket with a waterproof hood, etc.
If you can have a friend, coach or fellow competitor hold an umbrella for you while you shoot and do the same for them when they shoot.
WIND
Studies show that the wind effects the archer more than the arrow by making you less steady on your feet. The wind is literally blowing you in one direction and you need to anchor your feet and stand firmly to your spot - unbending like an oak tree. Master this ability to be unmoving despite the wind blowing you and the simple matter of adjusting your arrow shots to match the wind will seem easy. (Building up your strength and balance in your legs will be an advantage in such conditions to help keep you steady.)
In wind conditions it depends on whether it is a steady wind or gusting.
A steady wind is easy to adjust for. It will knock your arrows sideways so you need to adjust your shots accordingly. I also find that heavier arrowheads make for less fishtailing arrows, so that will improve your accuracy.
A gusting wind means you need to be patient and time your shot between the gusts. A technique I use is to study the grass while waiting to make my shot. If the grass stops moving in the wind momentarily then it is the right time to shoot. You will still need to adjust your shot like during a steady wind, but the random gusts will feel less random.
If you don't learn how to adjust for both steady and gusting wind then good luck. Your shots will be a lot more random because you lack the experience learning how to adjust your shots. Experience and training yourself in these conditions are the biggest factors for improving your ability to shoot.
Let your arrows tell you where to aim. This is an old school traditional archery thing, but it remains true for all time. If your shots are going to the left then shoot to the right the appropriate distance. Do NOT changes your sights on your bow. The reason is because if the wind changes several times during the competition then you won't be able to remember all the changes you made.
Shifting Wind Conditions - These are the worst. The wind keeps changing direction at random, sometimes changing and then changing again within mere seconds. Remember your training however and learn to shoot in-between the gaps when the grass it still.
During competitions remember that your fellow competitors are having the same problems as you are. If you have trained to shoot in wind and rain then you will be fine. If they haven't then that gives you a competitive edge.
Many archers have less problems combating extreme heat and humidity because they are used to training outdoors on hot days. A lot of this you should already know. However for the purpose of diversity here is some tips.
Drink lots of fluids - Powerade, Gatorade, juice, etc. Avoid caffeine and alcohol. Avoid sugary drinks too.
Learn the warning signs of heat fatigue, heat exhaustion and heat stroke. Not just for you, but for your fellow competitors.
Keep ice packs and cold drinks in a cooler. A personal cooling device (like those backpacks that cyclists wear) would be handy too. Apply cold packs to your neck and other areas where blood flows.
A fun thing to bring is a camping shower device. Fill it with cold water and stand under it for a cool shower.
Wear clothing that doesn't trap heat or sweat.
Stay in the shade whenever not shooting. A large beach umbrella would be handy if there is no shade available.
