Quick note - it is not the speed of sound in the gas that affects a person's voice, it is the density of the gas that affects resonance. Speed of sound usually correlates with gas density if the pressure remains equal, however, so it is easy to conflate the cause there.

Gas density will also affect how Bernoulli's principle causes your vocal cords to vibrate - a less dense gas will lessen the effect of Bernoulli's principle, which is responsible for pulling your vocal cords into the moving airstream - but this is counterbalanced by the fact that it also offers less physical resistance to your cords springing back and forth, and that it requires less effort for your diaphragm and lungs to expel. The result is that more gas volume will be expelled for a given amount of effort i.e. your lungs will push out the air faster if you do not consciously compensate, thereby increasing the effect of Bernoulli's principle. So these two effects more or less cancel out and the fundamental pitch and amplitude of a person's voice will remain basically consistent.

Rather, it is the resonant characteristics of your head and chest, which give your voice its unique timbre, and distinguish it from another person's voice (and indeed from a piano or violin), which will be noticeably affected.