It changes.
The small muscles and cartilages in your vocal apparatus aren't immune to aging. Also, as your visage loses tone and becomes flabbish, your soft (everything not made of bone) resonators change, and so does your sound. Usually you get to keep your "twang", but it's slightly muffled by a small loss of high harmonics.
Furthermore, your ear can lose a step or two and - since we innately modulate our emission with our ears - The vocal production will be tainted by a kind of "false" sound image from the source, so to speak.
The entity of change depends on many indirect factors too. For example:
How you deal with ASL, that is Alcohol, Smoke, Lack of sleep.
Your small muscles tone. The more you exercise and the more your vocal training revolves on the operatic style, the more you tend to speak in a fixed position (the same you sing with), the more your speaking voice fends aging away.
The way you speak and the percentage of soundless air you use in your spoken voice. Without entering the field of speech therapy, air and wrong posture can destroy your sound as soon as you body ages, and even before that.
The subject is obviously more complex and I'm horribly simplifying it, but I wanted to respond to your curiosity and not to bore.