You're not accessing it from inside the class, you're trying to access the variable as though it were public. You would not expect this to compile, and this is pretty much what you are trying to do:
public class SomethingElse
{
public void CallHowdy()
{
A a = new A();
Console.WriteLine(a.Howdy);
}
}
There is no relationship, and it sounds like you are confused why that field is not public.
Now, you could do this, if you wanted to:
public class B : A
{
public void CallHowdy()
{
Console.Writeline(Howdy);
}
}
Because B has inherited the data from A in this instance.