Users who perform welding on machinery are not necessary diligent in taking precautions like disconnecting the battery from the vehicle. Apparently, welding can cause severe damage to the electronics.
So:
EDIT: The question was referring to arc welding.
First and foremost, major props to Optionparty and John U who pretty much already nailed it.
The welding action itself is a brutally noisy high amperage DC current applied to the body or frame of the vehicle. In a perfect world, the battery would be disconnect, no current would be flowing in its systems, and the welder would have an extremely short path to its return ground, with no stray currents. In the real world, the battery is in, the car is on, and the ground lead stays in one spot on the other side of the vehicle while the welder goes all over the place.
Since the vehicle's body and frame is the ground reference for the onboard systems, its pretty conductive, and the potential for EM broadcast is massive. This high frequency broadcast could scramble control signals in computers by induction directly over those signals, or by inducing noise between the input power line and ground. A Faraday cage around the device could very well be a solution, except that you don't have access to an actual earth ground, and you don't want to reference it to the car's ground, because, well, welder. It's not a problem, it's a consideration - you have to leave the Faraday cage floating, which means any received EM will be rebroadcast on the other side of the cage.
Radio frequency chokes on input leads will prevent anything wild from getting into the power supply circuit for your electronics. Shunt capacitors should also help, but I would put them before the choke, in the event a stray current decides to take a path up the shunt cap into the power line - it shouldn't happen but, hey, the battery should have been disconnected, right?
If your device takes in small gauge instrumentation signals from other places, you probably want to do two things. One, specify shielded wiring. And two, isolate that signal from the actual receiver, using a capacitive or optical isolation IC. The shielding is a bit double edged. You want it to protect the inbound signal from high frequency corruption and cross talk, but now it stands a chance of becoming a stray path. The isolation can protect you to something like 2500V, pretty cheaply. So hopefully the worst case scenario now is that the input becomes incomprehensible garbage, which the circuit should be reasonably ready to reject.
And fuses. Don't forget fuses. Fuses are your friend. Or resettable polyfuses, if appropriate.
Arc welding uses power from a Power Co. Transformer; with a grounded case and leg(one end of the transformer output). The Arc Welder also has a transformer with a grounded case and leg. The two cases/legs must be grounded together or a difference of potential exist under load. This difference of potential can be known as Stray Voltage of Floating voltage/current. When not sharing case and earth grounds, there can be damage to small voltage/current devices.
Today's computers, sensors, and microscopic gold wiring terminations inside processor chips will and can burn open. I have witnessed $1,000,000.00 damage to electronic components on Navy Ships in a single day of welding.
Computers terminals catching fire due to welding equipment using the same power source. Burnt electronic components in weapons, satellites transceivers, and computer equipment. Ground your welding equipment to the hull with the existing lead, the common transformer ground via the power input cable, and a grounding strap from the welding case to hull or earth.
Still a potential damage from welding exists due to better paths of current returns. If the welding equipment lead ground is not the best return path; such as further from the weld point than a copper path thru any local grounding circuit, damage can occur to components. Example:local power has an electronic component sharing the welding source of power; the arc finds current path thru the copper ground of the local components versus the 50-300 foot weld ground lead back it's transformer ground/and path to it's power source ground.
Today's grounding technics do not met the requirements of today's miniature circuits and it is not a question of a welder's perspective.
