How to change default text color using custom theme?

In your Manifest you need to reference the name of the style that has the text color item inside it. Right now you are just referencing an empty style. So in your theme.xml do only this style:

<style name="Theme" parent="@android:style/TextAppearance">
    <item name="android:textColor">#ffffffff</item>
</style>

And keep you reference to in the Manifest the same (android:theme="@style/Theme")

EDIT:

theme.xml:

<style name="MyTheme" parent="@android:style/TextAppearance">
    <item name="android:textColor">#ffffffff</item>
    <item name="android:textSize">12dp</item>
</style>

Manifest:

<application
    android:icon="@drawable/icon"
    android:label="@string/app_name"
    android:theme="@style/MyTheme">

Notice I combine the text color and size into the same style. Also, I changed the name of the theme to MyTheme and am now referencing that in the Manifest. And I changed to @android:style/TextAppearance for the parent value.