First of all, Vader doesn't rush headlong into battle anymore like he used to as Anakin - and he survived that. These days, he sends expendable stormtroopers to overrun the enemy and secure the ground before making his entrance. If anyone is dead from a trap, it won't be him.
Secondly, even if something is amiss, that is exactly what the Force is for. It gives Force wielders like Vader extrasensory perception and limited, usually subconscious foresight into the future, all of which help keep him alive. Where it's unavoidable - for instance, exploding AT-RTs falling on him (Rebels Season 2 pilot movie episode), it does give him the forewarning needed to react and protect himself by levitating the debris from direct impact. This is a skill demonstrated by Jedi too on the likes of collapsing caverns etc, not unlike those on Hoth.
Thirdly, don't underestimate Vader's suit. It is a pressurised environmental suit, capable of surviving in the vacuum of space and can perform better in all terrains than specialised stormtroopers (eg. Snowtroopers). It is also well-armoured against damage, including substantial resistance against even lightsabers. That suit can take quite a lot of punishment.
So far, this answers why it is ok for Vader to enter enemy territory - the risks are tolerable. The next question to answer is: Why?
Vader is not an armchair general. He is the Emperor's first weapon of terror. The aura of the dark side emanating from him naturally strikes fear and dread in those around him, even if they aren't Force sensitive. Effective use of such a weapon - whether to drive the Imperial troops forward or to scatter the Rebels into retreat - requires Vader to be visible at the frontlines.
In Legends lies another part of the answer. In Vader we can glimpse the slightest hint of Anakin Skywalker persisting as the Jedi General who leads his men from the front. Despite their fear, his stormtroopers are fiercely loyal to him, for "he will not tell us to do anything he will not do himself".