(I'm going to move this into General, as Rally Point is mostly for people looking to meet up with other shooters)
I'm not in the mil or popo but if shooting is practical for you and not just a fair weather hobby, then you for sure need to shoot in all kinds of weather. i used to shoot in the snow any chance I got because it doesn't snow much here. i even drove to shoot in a hurricane once.
For Rifles:
Shooting in inclement weather definitely makes a big difference with rifles. There are a lot of things you will figure out really quick. For example, you probably never noticed but you're breathing all over your rifle all the time. Exhale once on your scope and the lens will be covered with moisture from your lungs which will freeze instantly when it hits the ocular lens, and you're done for the day, or at least until you can bring the temp of the gun up above freezing and then clean the lens.
little things like your hot spent brass ejecting into the snow. melts everything it touches for a few seconds and then all that water freezes and keeps it from going back in it's proper hole in the ammo box. if you can find it under the snow...
the cold affects your ballistics a couple ways. cold powder has less energy, and cold air is more dense. at distance, you will hit significantly lower than in hot weather. most ballistic calculators compensate for it, but pay attention if you're shooting past 400 yards or so.
figuring out how to wear gloves and keep your trigger pull consistent can be a challenge. most people wind up modifying their glove.
and gloves are important because cold metal will suck the warmth out of you fast.
most of cold weather shooting is just managing your gear when everything is more awkward. like you can't set your range finder or binos down, or
ammo box, etc.
if you get REALLY cold, you may need to change your lube.
my recommendation is to keep the gear at ambient temp as well. You may be tempted to bring the rifles in to keep them warm and then take them out in the cold when you go out to shoot. that's usually a mistake. the scopes will fog, and if you set the rifle down in the snow, it will melt and then refreeze and could lock your action up with ice. leave them outside overnight and you won't have a problem with the scopes fogging, unless you breathe on them...
if you shoot prone in the snow
-shooting a muzzle brake will create a mini blizzard
-you'll need more bipod than you usually use
-try to keep snow out of your magazines
For Pistols, it was never really much different for me, other than my fav cold weather clothes interferes with my fav holster, but maybe someone else has different experience
oh, and practice mag changes with retention lol