Kept clean and lightly lubed, should be good in any part of the country, any season.
YAAAABSOLUTELY !
While your firearm is under your clothing, it remains nicely warmed and thus when removed, will cool down and shed any moisture that has built.
Unless you DO spend a good bit of your time wallowing in drifts and sloshing about in the cold drizzling sleet, it will stay nice and dry inside your clothing. If THAT SLOPPING is the case, a wipe-down with an oily rag and an occasional blast with some sort of gunk-scrubber will keep things aright.
As has been mentioned, perfect your draw and presentation, don't fail to practice in bad weather - develop your presentation skills for the clothing and situation. If you are wearing a sweater and a long topcoat, an IWB rig is a difficult start. Nothing like a big gob of sleet smack in the middle of your rear sight to spoil your careful aim, and especially if your fingers are stiff and cold and the wind is 40 knots sideways, too. If you wear glasses, a hat with a brim to keep snow and rain off the glasses should be a part of your outfit, too. Practice, practice, practice.