Ok so this gets into something specific about barrels, where you wouldn't drag it, you would roll it. Which, theoretically you could do that stealthily - under the right conditions.
However, as DM I would insist - and this is SUPER important - that you play the right Theme Music while doing it.
Otherwise you go at disadvantage. :P
While you can roll a barrel around, it's still going to be unwieldy and loud. You certainly aren't going to be ducking between shadows with this thing. Are there situations where you could move unnoticed with one? Probably, but I imagine they'd be uncommon.
Also, the appropriate theme music for BG3 is this.
I don't know where you are getting your barrels but I think you need to fire your Cooper -- or you are thinking of metal barrels.
Wooden barrels are pretty quiet, on a flat surface anyway, if they have been made right and balanced, sanded, filled and closed correctly.
Good tip is to make sure the floor is clean and swept.
Frankly if they are going with barrelmancy they should just make it into a class.
Barrelmancer- D8 Hit die. Starting equipment is a ramp, broom, metal rings, spare boards, and sandpaper. Create a new class skill called "stealth barrel". You have a set of clips that lets you carry a single barrel on your back. Min strength is 16. You use dex and strength to determine throw accuracy. At Fifth level you get Tensers Floating Disk at will so you can carry a second barrel. Due to the barrel on your back you cannot use any melee weapons, only a special crossbow that is anchored to your chest and can only be fired every other round with a huge arbalest-like bolt that does 3d6 damage.
There is a 10% chance every time you throw a barrel that you suffer 2d6 damage from throwing out your back.
