Do you want a class that is a collection of textboxes? Or a customized textboxes?
An array and a class is a really different thing.
When you add a control to another (i.e.: if you add a textbox to a panel), .NET will set the parent of the panel automaticly. There is no need or no use of setting a parent, since it's being set as you add a control to another.
Wouldn't it be easier to put the textboxes on your form at designer time then jsut store the string values to display in your class? You're going to make a lot of work for yourself if you want to draw the textboxes from your class on to your form.