If you have a specific shape in mind and can create a sketch to represent that shape, you are halfway to your goal.

The concept is simple. Create a single line sketch that would represent the desired curve, starting from, in this example, the nose of the cone and traveling to the base. Create only one-half of the nose cone curve and maintain a "standard" axis reference, say, using the Y-axis as the rotation point.

The process is called revolve. Fusion 360 supports this action directly.

In the Sculpt workspace, choose Create Revolve.
Select the profile to revolve.
In the Revolve dialog:
    Click Axis and then select the axis to revolve around.
    Choose Full or Angle to specify whether the revolution is full or to a specific angle.
    For Direction choose One Side, Two Side or Symmetrical.
    For Symmetry, choose None or Circular.

The above text is taken directly from the link. The specific web site also includes a Flash video of the steps involved.

If thickness is required for your creation, consider to draw the sketch from the nose to the base, then use Offset or hand sketch in a parallel line that returns to the nose. Ensure the base segment is joined and that the nose segments are open and are aligned to the Y-axis.

As the sketch is revolved, the nose sections will "close" while the base creates the closure necessary to make a solid that is hollow within and open at the bottom.

Use The Google or your preferred search engine with the terms "Fusion 360 Revolve" to find many tutorials and videos with the same information presented in various ways.