Can I write a class using PowerShell?

Take a look at the Add-Type cmdlet. It lets you write C# and other code in PowerShell.
For example (from the above link), in a PowerShell window,

$source = @"
public class BasicTest
{
    public static int Add(int a, int b)
    {
        return (a + b);
    }

    public int Multiply(int a, int b)
    {
        return (a * b);
    }
}
"@

Add-Type -TypeDefinition $source

[BasicTest]::Add(4, 3)

$basicTestObject = New-Object BasicTest
$basicTestObject.Multiply(5, 2)