Metal Gear Solid lead actor David Hayter says he intentionally didn't try to mimic Snake's inspiration when creating the voice for the character.
Speaking to Fall Damage, Hayter says, "When we started Metal Gear and I started taking on Snake, I didn't want him to sound like Kurt Russell from Escape from New York." He explains: "I knew that there were similarities there and I felt like he needed to sound more weathered, you know, that he had been through a lot more than I had been through at that point in my life."
Russell played the character Snake Plissken in the film, a mullet-donning, cigarette-smoking, eyepatch-wearing badass, to which Hideo Kojima was clearly inspired for both Solid Snake and Big Boss. He even acknowledged this, with Metal Gear Solid 2 introducing Iroquois Pliskin a character who looks suspiciously like Solid Snake (but it couldn't be, he died on that tanker two years ago).
Before Hayter was replaced as Big Boss – with Kiefer Sutherland playing the role in Metal Gear Solid 5: Ground Zeroes – Kojima actually tried to get Kurt Russell himself to play the character in Metal Gear Solid 3. Escape from New York director John Carpenter also revealed that the studio wanted to go after the game for ripping off the film, but "I told them not to do that. I know the director of those games, and he's a nice guy, or at least he's nice to me."
Hayter has a point, though, while Metal Gear Solid was many people's entry point to the franchise, Solid Snake was already in retirement by the time that game took place, with the original MSX2 games taking place 10 and six years before the PS1 title (where he would get a voice for the first time). So, the weathered take on the character was probably the right one, and would prove to be one of the most iconic voices in gaming.
