Is there any way to generate a Curve class and then draw that curve in 2D on the screen in XNA?
I want to basically randomly generate some terrain using the Curve and then draw it. Hoping that I can then use that curve to detect collision with the ground.
It sounds like what you want is the 2D equivalent of a height-map. I'd avoid making a true "curve" and simply approximate one with line segments.
So basically you'll have an array or list of numbers that represent the height of your terrain at a series evenly spaced (horizontally) points. When you need a height between two points, you simply linearly interpolate between the two.
To generate it - you could set a few points randomly, and then do some form of smooth interpolation to set the rest. (It really depends on what kind of curve you want.)
To render it you could then just use a triangle strip. Each point in your height-map will have two vertices associated with it - one at the bottom of the screen, the other at the height of that point in the height-map.
To do collision detection - the easiest way is to have your objects be a single point (it sounds like you're making a artillery game like Scorched Earth) - simply take the X position of your object, get the Y position of your terrain at that X position, if the Y position of your object is below the terrain, set it so that it is on the terrain's surface.
That's the rough guide, anyway :)