Or is it better to leave it on?

Obviously we're ignoring all social norms and medical advice and just talking from a pure physics perspective.

And in physics, there are two main ways you can use water alone to cool something down. 

The first water cooling method is to run cool water over or through the hot object so the water warms up and takes away the heat, and therefore, cools the object down.

This direct transfer of heat is the basic idea behind the radiators in car engines, liquid cooling of fancy gaming computers, and water cooling of power plants.

For a human being, this would mean drinking, say, a liter of freezing-cold water every hour, letting your body heat the water up to body temperature, and then removing it from your body by urinating or sweating and then wiping off the sweat.

A liter of water can move 1 calorie of heat per degree Celsius it heats up, so using water for liquid cooling can remove at most around 37 Calories of heat every hour

One calorie for every degree Celsius between freezing and body temperature.

The second water cooling method is to put water on the object and let it evaporate.

A liter of water, to evaporate, absorbs around 540 calories of heat, which is a lot more than the 37 Calories removed by drinking and urinating ice water.

But a human body can't necessarily evaporate a liter of water every hour: a square meter, under room temperature conditions, will only evaporate about a third of a liter per hour, and the surface area of a human is only between 1 and 2 square meters. 

So we could expect a sweaty human body to lose at most maybe 180-360 Calories of heat every hour from evaporative cooling.

Which is still 5 to 10 times more cooling power than liquid cooling.

Obviously, evaporation is also super condition-dependent: if it's hotter or windier or drier, then the power of evaporative cooling increases substantially, while if it's cooler or more humid then evaporation is less effective. 

But either way, it seems pretty safe to say that for human bodies, evaporative cooling is far more effective than liquid cooling.

In other words, letting your sweat evaporate is far more effective than wiping it off.

Which actually isn't that surprising: sweating is our evolutionary means of cooling off, so perhaps it's not surprising that letting your body do its thing turns out to be a good idea, but it's amazing how effective it really is. 

And luckily your body can use both methods of water cooling.

If you drink cold water, you benefit from direct heat transfer while your body warms the water up to body temperature, and then you benefit from evaporative cooling when the water evaporates as sweat. 

And physics doesn't completely prohibit wiping off your sweat.

If sweat is literally dripping off of you, a) it's not going to help evaporatively cool you once it's on the ground, and b) chances are you're producing sweat faster than it can evaporate.

So it's probably ok to wipe some of the sweat off - or perhaps better yet, smear it around to make sure it has the most surface area possible for the most effective cooling!

As a reminder - nothing in this video constitutes medical or hygiene advice.

But if your sweat is dripping, it's much better – for the purposes of evaporative cooling – to smear it around rather than wipe it off entirely.

And if you're hot and sweaty but it's not dripping, physics says "leave it on."