Well, usually welders wear leather gloves, which are good insulation.
Also, the electrode holder or the welding gun is usually covered with plastic insulation as well. It's not bare metal,
Normal welding voltage is only around 18-27 volts. (it surprises me how many experienced welders don't know this.) This is much less than household current which is 110 volts. In other words, welding uses very high CURRENT, but low VOLTAGE. Under normal circumstances, welding voltage is not dangerous.
It would take quite a lot of consecutive bad judgments, before you'd be in danger of electrocution from a welder. (I won't say it's never happened though....)
It is HIGH VOLTAGE which makes electricity dangerous, not high current. Dry human skin is a very good insulator. so it takes high voltage to overcome the resistance of the skin.
To understand why this is, I'll indulge you with a little physics. The relationship between voltage and current is known as "Ohm's Law:"
V / R = I
Where V is voltage, R is resistance, and I is current.
The resistance from hand to hand in a human body can vary a lot. With welding gloves on, I'd estimate that to be > 100,000 ohm. So even at 28 volts, the current would be only
28 / 100,000 = 0.00028 amps.
This is far too little current to even be FELT!
It generally takes about 0.005 amps to be picked up by the nerves, .06 amps is very painful and potentially dangerous, whereas it would take 0.2 - 1.0 amps to be seriously life threatening, This much current would also cause immediate unconsciousness.
With your welding gloves off, with sweaty hands, touching bare metal, your resistance could go down to around 1500 ohms. So,
28/1500 = 0.02 amps.
This is in the range of painful, but not very dangerous. Note: this has happened to me a few times, 'cause I'm an idiot.
Hope that makes sense.