Yesterday evening I passed on a shot at a stag at 190 yards because it was raining very heavily plus a strong headwind. I was worried that the two together could slow the bullet.
So does heavy rain slow the bullet?
In your scenario, almost certainly not.
Firstly headwinds, and tail winds have almost no effect on trajectory. It is the cross wind component that matters. Your bullet is flying at, lets guess, something like 3000 fps. Which is 2046 mph. So even if you have say a force 8 gale blowing (about 40 mph) as long as it is directly along the bullet's path, it is practically irrelevant. However wind can swirl about, so what may seem entirely "in your face" at the firing point could be entirely different further away.
Next, the rain. Your 190 yard shot. Again at say 3000 fps the flight time of your bullet might be 0.2 seconds. What are the chances of it hitting a big raindrop, sufficient to cause a deflection, in that time ? If you drive a car down the road in teeming rain, how much of that actually hits the windscreen in 0.2 seconds ? How fast do your wiper blades sweep it away ?
Thirdly, atmospheric considerations. Generally, here, rainstorms are associated with low pressure. Which makes the air less dense, so bullets (at longer ranges) will rise, not fall.
Fourthly, in heavy storms, atmospheric humidity is pretty much 100%. Which (maybe counter-intuitively until you understand) reduces the air density. Bullets again will fly higher, not lower. Just as in extremely low humidity, air becomes denser and bullets drop.
Long range target (paper or furry) types need to consider the atmospherics primarily. Shooting a stag at 190 yards, far less so.
Considerations should be whether you are comfortable taking the shot, not soaked to the skin, cold, the rifle slippery in the hands, the 'scope, and spectacles beaded or dripping with water (good coatings, for both riflescope and glasses, if you wear them, make a huge difference, as does a wide brimmed hat)
Then water running down inside the barrel, or filling up the mod. Stop that by e.g. taping it over, use a condom, or even one of the fancy orange silicone re-usable plugs that Mauser used to sell for this purpose.
Next question might be whether taping or otherwise sealing the muzzle against water affects accuracy. All that I can say is it seems not, based on some mucking about on the range with the club. Electrical tape, even two layers of gaffer tape, the condom, and even a disposable foam earplug (the club .308 took on that challenge, it was pretty much shot out anyway) had no discernible effect. The club 308 survived unscathed, three times, as did the earplugs Recovered within a few metres, all looking good as new.
this is an interesting article on the effects of wind, ie cross, head, vertical and horizontal winds. My take from this is that there is little effect on 100yds compared to 600yds
www.sierrabullets.com
This one on the effects of rain, suggests that rain does indeed have an impact and the rain does hit bullets in motion
Does shooting in the rain affect a bullet's trajectory?
www.gunsandammo.com
Actually I thing the gunsandammo article concludes quite differently. The experimental setup was purpose designed to image a bullet actually hitting a raindrop, which they cleverly managed to do, but tells very little about the chances of that happening in reality.
Here is another one
An Official Journal Of The NRA | Does Rain Lower Your Bullet's Point of Impact?
What really can mess up a shot though is deflection from even a grass blade, leaf, plant stalk, twig or other such thing. Shooting prone off a bipod, or using a high mag. scope that can't focus on nearer objects does not help. And no "brush buster" chamberings are something of a myth.