Customizable Modular Snowman

Goals:
1) To derive all of the dimensions for any size snowman from a single parameter, the diameter of the bottom snowball.
2) To have the ability to print a snowman in one piece or multiple pieces.
3) To force all vertical dimensions to be an exact multiple of the chosen printer layer height and all horizontal dimensions to be an exact multiple of the chosen nozzle diameter.
4) Continue to develop my openSCAD programming skills.

There are two main parameters, the desired part name and the desired diameter of the bottom snowman. The part names are:
"man" -> Complete snowman with a hat on top.
"body" -> Complete body with a peg on the top.
"hat" -> A hat with a peg hole on the bottom.
"botmid" -> Combined bottom and middle snowballs with a peg on top.
"midtop" -> Combined middle and top snowballs with a peg hole on the bottom and a peg on the top.
"bot" -> A bottom snowball with a peg on the top.
"mid" -> A middle snowball with a peg hole on the bottom and