Swimming or treading water requires dropping or stowing any heavy or bulky objects being held, including shields.
Medium or heavily armored characters must make a DC 13 Athletics check at the start of each 10-minute turn, gaining a level of Exhaustion on failure. Failing by 5 or more indicates that by the end of that turn the PC will no longer be able to effectively tread water, at which point the standard breath holding and suffocation rules kick in.
A standard backpack at or near its 30lb. capacity causes those same penalties to swimming.
A character can doff and drop his or her armor at any point to end these checks.
Unarmored or lightly armored characters (without levels of exhaustion) can Help, granting advantage on the check, but they too will gain a level of exhaustion if the check fails.