How do I disable or slow down the mouse?

Here's a possibility:

1) Set a timer for say 25ms.
2) Get the mouse position with GetCurPos.
3) Store the values in some variables.
4) In the next call to the timer function, get the cursor points again.
5) Calculate the change in x and y values.
6) Divide the change by some number (the larger the number, the slower the mouse will move).
7) Set the new position to the old position plus the change in coordinates divided by the magic number.

Now, I am no professional, my logic is probably flawed somewhere along the line... perhaps I will test it and let you know what happens.

Forgot to add that the function that you use to set the new coordinates is SetCurPos.

To get two mouse threshold values and the mouse speed, call:
SystemParametersInfo(SPI_GETMOUSE,0,&buf,0);
with buf is an array of 3 integers to store these values.
Then change the value of buf, and call:
SystemParametersInfo(SPI_SETMOUSE,0,&buf,0);

These function is in USER32.LIB (#include winuser.h)

I'm sorry, if you declare:
int buf[3];
then you have to call:

SystemParametersInfo(SPI_GETMOUSE,0,buf,0);
//not    &buf

This is a very good answer, but I've tried it already with disappointing results.  The cursor did seem to slow down but the best I could get was about a 50% reduction in cursor speed. I tried values from 0 to 300 in the 3rd element (i.e. buf[2] = 0).
Do you know of any way to totally freeze, hide or disable the cursor?

If all you want to do is freeze the mouse, I know of a much simpler way.

Use:
RECT rect;
POINT point;

GetCursorPos (&point);

rect.top = point.y;
rect.left = point.x;
rect.bottom = point.y;
rect.right = point.x;

ClipCursor (rect);

I think that ought to do it.

Then, to allow the cursor to resume moving, do the same thing only in the RECT structure, fill in the screen resolution, i.e. 0, 0, 640, 480.

JKR's answer looks like it will work for my situation, THANKS.