I inherited a couple boxes of Winchester ammo labeled, ".30 Army Full Patch."

I understand these rounds are the same as .30-40 Krag and the Full Patch wording refers to the practice of wrapping undersized bullets in paper as part of the assembly process.

Since the ammo I have shows no exposed paper, I'm wondering if it has come off, or am I missing something?

full patch refers to the bullets being full metal jacketed as opposed to lead. No paper involved

There's no paper, just an old fashioned way of saying "full metal jacket."

Old Tanker, my boxes look just like yours. On the top label, there are some numbers on the bottom right. Is this the manufacturing date? If not, do you have any idea how old this ammo is?

I read that paper patching was the forerunner to full metal jacketing. It makes sense that Winchester would use that term to eliminate potential customers' concerns.

I believe that's when that particular packaging style / label was introduced.

__________________
"I also cook."

I do not know if that is a date code or not, although it looks like it might be. Odds are it is "pre-war", your guess is as good as mine if that means the "Great War" or WW2. Primers are most probably corrosive, and possibly mercuric as well. Some ammo collector likely knows. I'd bet you'd be better off displaying it next to your '95 Winchester that putting it through it.

Full patch has long been used to refer to full-metal jacket bullets. If they are silvery looking metal it is cupronickel and will foul barrels badly with a very stubborn and lumpy fouling.

"Ordnance Department Metal Fouling Solution" ,commonly known as "Ammonia Dope". was used to dissolve the metal fouling by the military, but it was tricky to use. The "dope" was poured into a rifle barrel with a "corked chamber". A piece of rubber tubing was placed over the muzzle to allow the dope to cover the muzzle and prevent any air getting to any metal exposed to the dope. Any contact with air would ruin the barrel within a few minutes.

The solution had to be made up fresh for each use. If the dope became "stale" it became corrosive to the barrel. After a 20-minute treatment, the solution had to be immediately poured from the bore. The bore was
then dried and oiled. This treatment dissolved the metal fouling and left the bore pristine for further firing. The recipe, just in case you want to know:

Ammonia Persulphate 1 ounce
Ammonia Carbonate 200 grains
Stronger Ammonia Water (28%) 6 ounces
Water 4 ounces

Gilding metal, an alloy of copper and zinc, had been considered too soft for a military bullet, hence the use of cupronickel. In 1922, the Western Cartridge Company overcame the disadvantages of straight gilding metal by adding 2% tin to the jacket. This gilding metal/tin jacket material became the famous Lubaloy Bullet Jacket. The Army's Franfort Arsenal came up with a similar jacket material about the same time.

I bought a few boxes of "30USA" which I believe is the same
thing you are talking about. It was empty brass but somewhat
heavier than standard 30/40. It had obviously been thru a rifle
due to the ejector cut on the heel. I got it to convert to 445
SuperMagnum, which I did. Heavy duty brass. Not suited to reading
pistol pressures An orphan now.

...Nemo...